University of GuilanJournal of Mathematical Modeling2345-394X14120260301Dynamic adaptation strategies for optimal control in unknown linear time-invariant system117887610.22124/jmm.2025.30264.2716ENHomaPouyanfarDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, IranSohrabEffatiDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, IranAminMansooriDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, IranJournal Article20250404This paper presents a framework for online adaptive optimal control of continuous-time linear systems with unknown dynamics. The approach uses approximate and adaptive dynamic programming to learn the optimal control policy and value function in real-time, without prior knowledge of the system matrices. We introduce two algorithms based on policy iteration and value iteration, providing proofs the convergence and stability. Our value iteration method is robust against from exploration noise. The effectiveness of these control strategies is demonstrated through two examples, highlighting their ability to achieve near-optimal performance despite unknown dynamics. https://jmm.guilan.ac.ir/article_8876_121fae0e0bfcfd9f477de65a53e5cff7.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301An accurate computational approach for solving system of differential equations involving non-local derivatives1934901010.22124/jmm.2025.30849.2765ENGauravSainiAssistant Professor
Center for Data Science, Department of Computer Science and Engineering, Siksha `O' Anusandhan (Deemed to be University)0009-0006-2298-9085BappaGhoshAssistant Professor
Center for Artificial Intelligence and Machine Learning
Department of Computer Science and Engineering, Siksha `O' Anusandhan (Deemed to be University)SunitaChandProfessor
Department of Mathematics, Siksha `O' Anusandhan (Deemed to be University)Journal Article20250601This paper addresses the numerical approximation of a system of differential equations involving fractional derivatives of arbitrary order. The derivatives are governed in the Caputo sense of orders $\alpha_i \in(0,1)$. Motivated by the complexity of modeling coupled fractional dynamics, an efficient numerical scheme based on the classical L1 discretization technique is developed. The proposed method effectively captures the behavior of the system across various fractional orders and parameter regimes. A rigorous convergence analysis confirms the consistency of the proposed technique and establishes a convergence rate of order $\min_{p}\{2 - \alpha_p\}$. Numerical experiments are conducted to validate the theoretical findings, demonstrating excellent agreement with exact solutions and confirming the computational efficiency of the approach. These results highlight the robustness of the proposed scheme for solving the differential system with memory effects.https://jmm.guilan.ac.ir/article_9010_8f4a3bc99e2afa8b34432a2d5480a49f.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301New non-radial models for merger and acquisition to achieve strong efficiency and MPSS without changing in the efficient frontier3555903410.22124/jmm.2025.30974.2781ENAli RezaFakharzadeh Jahromishiraz university of technologyHassanRostamzadehDepartment of OR, Faculty of Mathematics, Shiraz University of Technology, Shiraz, IranJournal Article20250618In this study, new models for the merger of two or more inefficient units are presented. The discussed mergers in this study are horizontal and acquisition mergers. In the presented models, unlike the previously presented models, the mergers are done non-radially; indeed, managers can manage each of the indicators separately in the presented new merger process. In this regard, efficient frontier of the production possibilities set does not change, and merger of several units does not affect the efficiency score of other decision-making units. Also, by merging via the new models one can obtain a strong efficient unit with the most productive scale size. The presented models are applied to the horizontal and acquisition merger of Iranian banks.https://jmm.guilan.ac.ir/article_9034_d3f7caae6f4681a0520844959494ce41.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Boundary value problems for singular iterative dynamic equations on time scales5774903810.22124/jmm.2025.28778.2559ENMulukuri VenkataRamakrishnaDepartment of Mathematics, Govt. Degree College, Sabbavaram, Anakapalli, 531035, IndiaShaik KaleshaValiJNTU Vizianagaram, AP, IndiaMahammadKhuddushAndhra UniversityJournal Article20241023This study explores an iterative system of singular three-point boundary value problems within the context of time scales. The objective is to identify conditions that guarantee the existence of countable positive solutions. The research employs Holder’s inequality and Krasnoselskii’s cone fixed point theorem, set within a Banach space framework, to derive the necessary criteria. The theoretical findings are illustrated through a practical example, highlighting the sufficiency of the derived conditions for ensuring multiple positive solutionshttps://jmm.guilan.ac.ir/article_9038_e45dfbe208719c17af48bf81c2877833.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Enhancing implied volatility forecasting: multi-model approaches for the S\&P500 index7591909610.22124/jmm.2025.29881.2667ENNavidehModarresiAllameh Tabataba&amp;amp;#039;i Universty, Department of MathematicsRezaKazemiAllameh Tabataba'i Universty, Department of MathematicsAlirezaMousaviAllameh Tabataba'i Universty, Department of MathematicsJournal Article20250219Implied volatility is a crucial indicator in financial markets, as it reflects market expectations of future volatility and serves as a cornerstone for option pricing, risk management, and asset allocation. Accurate tracking and forecasting of implied volatility are essential for investors and portfolio managers to optimize returns and manage risks effectively. <br />This paper explores several modeling approaches for forecasting the implied volatility of the S\&P 500 index, focusing on exponential autoregressive conditional heteroskedasticity (EGARCH), long short-term memory (LSTM) neural networks, and a non-linear autoregressive model with exogenous inputs (NARX). In addition, a rough fractional stochastic volatility (RFSV) model is also examined. The empirical study demonstrates that the LSTM model offers superior forecasting performance compared to EGARCH, NARX, and RFSV. These findings have important implications for practitioners and researchers aiming to enhance risk management and trading strategies.https://jmm.guilan.ac.ir/article_9096_1e42ecafa3d9381b839b78d256c1a258.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301A predictor based method for signal detection in time series case study: financial markets of Iran in COVID-19 outbreak93114908610.22124/jmm.2025.29826.2666ENAmir HosseinGhatariDepartment of Statistics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran.Seyed RezaSeyed Ali MortezaeiDepartment of Statistics, Shahid Beheshti University, Tehran, Iran.MinaAminghafariDepartment of Mathematics and Statistics, University of Calgary, Calgary, Canada.0000-0002-9887-8385Journal Article20250218In this paper, we propose a signal detection method in time series data within the context of the financial markets. By analyzing historical data from the related markets, such as foreign exchange rates and cryptocurrency prices, we aim to identify significant signals affecting the cash price of refined Gold in the Iranian market. Our approach leverages various time series models, including autoregressive integrated moving average, seasonal autoregressive integrated moving average, and neural networks, and also regression-based time series methods to predict fluctuations in Gold prices. We focus on a working days period before and after the onset of the COVID-19 outbreak in Iran on February 23, 2020. To achieve this, we propose a predictor-based algorithm for signal detection that utilizes both traditional time series and regression models. This algorithm identifies auxiliary markets that correlate with the target market, fits appropriate models to predict future values, and then determines cloud confidence intervals around these predictions. Observations that deviate significantly from these intervals are flagged as potential signals, suggesting unexpected changes or trends in the target market. Our method not only enhances the ability to detect significant signals in financial markets but also provides a valuable tool for investors and analysts to anticipate and respond to market fluctuations, particularly during periods of economic instability, ultimately contributing to more informed decision-making and risk mitigation strategies.https://jmm.guilan.ac.ir/article_9086_61bdde634c7767545e8cfd4708342680.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301A theoretical study for air pollution model as a free boundary problem115135909310.22124/jmm.2025.29478.2618ENKarimIvazFaculty of Mathematical Sciences, University of Tabriz, Tabriz, IranGaderDarkhoshiFaculty of Mathematical Sciences, University of Tabriz, Tabriz, IranJournal Article20250105This paper presents a theoretical investigation of an air pollution model formulated as a free boundary problem. The study examines the dynamics of pollutant dispersion in the atmosphere, where the boundaries of the polluted region are not fixed but evolve over time. Using advanced mathematical techniques and partial differential equations, we construct a model that accounts for various factors influencing air pollution, including emission sources, meteorological conditions, and chemical reactions. The incorporation of a free boundary framework provides a more realistic representation of pollutant spread and environmental interactions. To analyze the model, we employ the Friedman-Rubinstein integral representation method and apply the Banach contraction theorem to solve an equivalent nonlinear Volterra integral equationhttps://jmm.guilan.ac.ir/article_9093_8749466cf63127b26ef7695bf67d0b4f.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Advanced bounds for eigenvalues in spectral fuzzy graph theory137160910410.22124/jmm.2025.29543.2628ENBuvaneswariRangasamyMATHEMATICS, SRI KRISHNA SRTS AND SCIENCE COLLEGE, COIMBATORE, TAMIL NADU, INDIASenbaga PriyaKaruppusamyFACULTY OF MATHEMATICS, DR. MAHALINGAM COLLEGE OF ENGINEERING AND TECHNOLOGY, COIMBATORE, TAMIL NADU, INDIASeyed AhmadEdalatpanahDepartment of Applied Mathematics,Ayandegan Institute of Higher Education,Tonekabon,Iran.Journal Article20250116This paper introduces advanced eigenvalue bounds for Spectral Fuzzy Graphs (SFGs), a subclass of fuzzy graphs with symmetric adjacency matrices enhancing the precision of spectral graph analysis. Leveraging the Rayleigh quotient and the Perron-Frobenius theorem, we establish novel upper and lower bounds for the largest and smallest eigenvalues of fuzzy adjacency matrices. Specific results include eigenvalue bounds for complete and bipartite fuzzy graphs, as well as the demonstration of eigenvalue stability under graph perturbations and unions. A numerical example based on a protein interaction network illustrates the practical applicability of the proposed methods, demonstrating improved accuracy in analyzing network resilience and connectivity.https://jmm.guilan.ac.ir/article_9104_2e9beb18ea1a260f1d7d613b2d2c4a04.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Tau-collocation method for weakly singular Volterra integral equations and related special cases161175909410.22124/jmm.2025.30587.2742ENSedaghatShahmoradDepartment of Applied Mathematics,
University of Tabriz, Tabriz-IranMahdiMostafazadehDepartment of Applied Mathematics, University of Tbariz, TabrizFevziErdoganDepartment of Mathematics, Van Uzuncu Yil University, Van, TurkeyJournal Article20250505The present study examines the implementation of the tau-collocation method for solving a class of Volterra integral equations and related cases which their kernels contain (special) weak singularity of type $(x^2-s^2)^{-1/2}$. These types of equations can be written in the form of the so-called \textit{cordial} Volterra integral equations and so inherit their properties. We will recall some conditions on the kernel and forcing function for which the existence and uniqueness of a solution has been proven. Then we will discuss regularity conditions for the solution of same types equations which indicate that unlike the standard Volterra integral equations with singularity of the form $(x-s)^{-\alpha}$, $0<\alpha<1$, these types of equations have regular solutions if the kernel and forcing functions are sufficiently smooth. This property allows us to use the classical Jacobi polynomials as a basis functions for collocation method. For this method, we will first derive a matrix formulation that makes it easy to implement. We will prove convergence of the method by providing an error bound.https://jmm.guilan.ac.ir/article_9094_4fc9d29d0d798536c0e26a59ed6413dc.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Proximal policy optimization with adaptive generalized advantage estimate: critic-aware refinements177190913210.22124/jmm.2025.29704.2654ENNaemehMohammadpourDepartment of Mechanical Engineering, Amirkabir University of Technology, Tehran, IranMeysamFoziDepartment of Computer Engineering, Amirkabir University of Technology, Tehran, IranMohammad MehdiEbadzadehDepartment of Computer Engineering, Amirkabir University of Technology, Tehran, IranAliAzimiDepartment of Mechanical Engineering, Amirkabir University of Technology, Tehran, IranAliKamali IglieDepartment of Mechanical Engineering, Amirkabir University of Technology, Tehran, IranJournal Article20250201Proximal Policy Optimization (PPO) is one of the most widely used methods in reinforcement learning, designed to optimize policy updates while maintaining training stability. However, in complex and high-dimensional environments, maintaining a suitable balance between bias and variance poses a significant challenge. The λ parameter in Generalized Advantage Estimation (GAE) influences this balance by controlling the trade-off between short-term and long-term return estimations. In this study, we propose a method for adaptive adjustment of the λ parameter, where λ is dynamically updated during training instead of remaining fixed. The updates are guided by internal learning signals such as the value function loss and Explained Variance—a statistical measure that reflects how accurately the critic estimates target returns. To further enhance training robustness, we incorporate a Policy Update Delay (PUD) mechanism to mitigate instability from overly frequent policy updates. The main objective of this approach is to reduce dependence on expensive and time-consuming hyperparameter tuning. By leveraging internal indicators from the learning process, the proposed method contributes to the development of more adaptive, stable, and generalizable reinforcement learning algorithms. To assess the effectiveness of the approach, experiments are conducted in four diverse and standard benchmark environments: Ant-v4, HalfCheetah-v4, and Humanoid-v4 from the OpenAI Gym, as well as Quadruped-Walk from the DeepMind Control Suite. The results demonstrate that the proposed method can substantially improve the performance and stability of PPO across these environments. Our implementation is publicly available at https://github.com/naempr/PPO-with-adaptive-GAE.https://jmm.guilan.ac.ir/article_9132_c7dfb26a364dde09244cec154dec609e.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Design of an optimal learning sliding mode control for linear systems191206932710.22124/jmm.2025.30152.2694ENMajidYarahmadiAddress: Iran, Lorestan, Khorramabad, Lorestan UniversityTaherehAzizpourDepartment of Mathematics and Computer, Lorestan university, Lorestan, IranJournal Article20250318In this paper, a new learning robust controller based on the sliding mode control method and reinforcement learning approach is designed for a class of SISO linear systems with a relative degree of uncertainty $ r$. For this purpose, a hybrid controller that including equivalent controller and learning robust controller, is designed. The proposed controller guarantees asymptotic stability, sliding condition, finite reaching time, elimination of chattering phenomenon and tracking of desired output in an optimally approach. For online approximation of the value function and design of an optimal policy a new robust optimal learning controller is designed. For analytical facilitation and stability analysis, three theorems are proved and a new algorithm is designed. Finally, a simulation example is presented to demonstrate the advantages of the proposed method. The simulation results show the optimality of the controls, the elimination of chattering phenomenon and the tracking of the desired output.https://jmm.guilan.ac.ir/article_9327_a00db244aaadd9edae34648d4a3904fd.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301A robust unsupervised feature selection based on subspace learning and adaptive graph structure207230912910.22124/jmm.2025.30225.2714ENHazhirSohrabiDepartment of Applied Mathematics, University of Kurdistan, Sanandaj, IranShahrokhEsmaeiliDepartment of Applied Mathematics, University of Kurdistan, Sanandaj, IranParhamMoradiSchool of Engineering, RMIT University, Melbourne, AustraliaJournal Article20250330Feature selection is vital for improving high-dimensional data analysis by identifying a subset of representative and uncorrelated features.<br />This paper presents an unsupervised feature selection algorithm based on subspace learning and adaptive graph structure (UFSAG).<br />The UFSAG uses matrix factorization to preserve global data structure and incorporates local correlations into its objective function.<br />It also integrates sample similarity graph learning to maintain data geometry.<br />Unlike prior methods, UFSAG employs adaptive local structure learning to reduce noise and enhance feature selection.<br />By inducing row sparsity in the feature coefficient matrix using the $\ell_{2,1}$-norm, UFSAG identifies representative features.<br />Comparative experiments on six datasets show UFSAG's superior clustering performance over twelve state-of-the-art methods.https://jmm.guilan.ac.ir/article_9129_51aea41a776790ee69c0f270bd847808.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301p-robust network cost efficiency with genetic algorithms and machine learning231251913310.22124/jmm.2025.30184.2705ENRitaShakouriDepartment of Computer Engineering, National University of Skills (NUS), Tehran, IranJournal Article20250420Original data envelopment analysis models for expected cost-efficiency evaluation lack robustness in the presence of uncertainty and high-dimensional data. This gap becomes more critical when dealing with big data in the petroleum industry, where selecting relevant variables from large, noisy datasets significantly affects performance results. To address this gap, we propose an uncertainty-integrated, two-stage network data envelopment analysis framework that incorporates artificial intelligence techniques, genetic algorithm and random forest for optimal feature selection. Genetic algorithm simulates natural selection to identify the most relevant variables, reducing dimensionality and enhancing model stability across probabilistic scenarios. In the second stage, Wilcoxon statistical testing and a p-robust approach are applied to ensure consistent and reliable ranking of decision-making units under uncertain conditions. Random forest complements this framework by capturing hidden data patterns, improving accuracy and interpretability. The model is validated using real-world data from ten oilfields, demonstrating substantial improvements over the traditional data envelopment analysis models in feature selection, expected cost-efficiency measurement, and decision robustness. This study offers a practical and intelligent decision-support tool for expected cost efficiency measurement under uncertainty in complex petroleum environments.https://jmm.guilan.ac.ir/article_9133_f01b192c17a51b452ee967ef0d80f8f1.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Numerical solution of the time fractional nonlinear burgers equation using the quintic B-Spline method253271914010.22124/jmm.2025.31069.2784ENFahad KamilNashmiDepartment of Mathematics, College of Science, University of Basrah, Basrah, Iraq.Bushra AzizTahaDepartment of Mathematics, College of Science, University of Basrah, Basrah, Iraq0000-0002-8282-9968Journal Article20250703This paper introduced a novel approach for resolving fractional partial differential equations.<br />The time fractional nonlinear Burgers equation of order k was solved to illustrate the efficacy<br />of the technique, where k in (0;1]. The quintic B-spline method facilitated spatial partitioning, while the finite difference method addressed the fractional Caputo derivative, which simulates anomalous diffusion processes influenced by memory effects. The proposed methods stability is demonstrated utilizing the von Neumann technique; it has been shown to be unconditionally stable. Additionally, a convergence study is shown, demonstrating that the approach exhibits uniform convergence of (gh4 +s(Dh2)). We validated the methods correctness through numerical tests by comparing it with the exact solution and alternative numerical methods. Based on L2 and L¥ error norms, the quintic B-spline approach exhibits improved convergence rates and reduced computing costs.https://jmm.guilan.ac.ir/article_9140_6451a05084b45f9c775a3874c9a3d2b4.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Numerical solution of Fredholm integral equations by the least squares method using QR decomposition273284915010.22124/jmm.2025.31188.2795ENMahdiAhmadiniaAlghadir Blvd University of QomMokhtarAbbasiAlghadir Blvd University of QomJournal Article20250715This paper presents a numerical method for solving the second-kind Fredholm integral equations using the least squares approach via QR decomposition. The proposed technique employs Gaussian quadrature for numerical integration and efficiently applies QR decomposition for minimization. This strategy not only simplifies the implementation but also significantly enhances computational performance. A convergence analysis is provided, and several numerical examples demonstrate the accuracy and effectiveness of the method compared to traditional technique.https://jmm.guilan.ac.ir/article_9150_a44d376538a70079f74d66f920f6045f.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Enhancing support vector machine performance through boundary-focused covariance matrix learning285304915910.22124/jmm.2025.30656.2746ENAfsanehPourmoeziUniversity of MazandaranAliTavakoliUniversity of MazandaranMostafaEslamiUniversity of MazandaranJournal Article20250514Support Vector Machine (SVM) has proven effective in various classification tasks by focusing on maximizing the margin between classes. However, standard SVM often fails to consider the underlying geometric structure of data near the decision boundary, particularly in scenarios where class overlap or noise occurs. This paper proposes a new method that focuses on boundary-critical samples those near the decision boundary by integrating their covariance matrix into the learning process. The principal eigenvector of this covariance matrix is then utilized to guide the classifier towards the most informative regions of the data, enabling it to capture the local geometry better. Importantly, this modification is confined to the objective function, ensuring the convexity of the optimization problem is preserved. Experimental results across various datasets, including linearly and non-linearly separable ones, demonstrate that the proposed method provides competitive or slightly improved classification performance.https://jmm.guilan.ac.ir/article_9159_a13c373ebee39a62a16169c704794d74.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Manipulability based model predictive control of rehabilitation robot305313917110.22124/jmm.2025.30154.2695ENAliPourmomtazFaculty of Mechanical Engineering, University of Guilan, Rasht, IranBehnamMiripour FardFaculty of Mechanical Engineering, University of Guilan.HamedKouhiFaculty of Mechanical Engineering, University of Guilan, Rasht, IranJournal Article20250318One challenge with rehabilitation exoskeletons is the potential for reaching singular configurations, reducing efficiency. Additionally, paths generated for an exoskeleton may not always exhibit optimal manipulability and dexterity, unlike healthy humans who perform tasks with maximum manipulability. This paper considers a multi-degree-of-freedom model for the exoskeleton robot, deriving its kinematic and dynamic equations. The robot's kinematic manipulability is formulated based on the Jacobian, and Model Predictive Control (MPC) is employed for control. The novelty lies in incorporating the cost function related to the robot's kinematic manipulability alongside other cost functions within the MPC framework. Dynamic simulations evaluate this approach, showing that the manipulability criterion conflicts with tracking error. This research demonstrates that using the manipulability index as a constraint or part of the cost function in MPC can help prevent the robot from reaching singular points and enhance manipulability and dexterity in hand rehabilitation.https://jmm.guilan.ac.ir/article_9171_d489bf78e8f6ea854fb201c3901830a3.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Spline-interpolation solution of Cauchy problem for a harmonic function in a simply connected 3D domain315325918910.22124/jmm.2025.29691.2646ENPyotrIvanshinKazan National Research Technical UniversityElenaShirokovaLobachevskiy Institute of Mathematics and Mechanics, Kazan Federal University, Kazan, RussiaJournal Article20250128Here we construct an approximate spline-interpolation solution of the Cauchy problem for the Laplace equation. Our construction describes two different methods based on solution of integral equations. The first method involves singular integral equation, and the second one is based on solution of a Fredholm equation. We present the linear and the polynomial examples clarifying the construction approaches.https://jmm.guilan.ac.ir/article_9189_e60054cc21388ba7c2ce51e2b9fb4a09.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Optimal control of a bioeconomic crop-energy system with energy reinvestment327346918710.22124/jmm.2025.31369.2815ENOthmanCherkaoui DekkakiCollege of Computing, Mohammed IV Polytechnic University, Benguerir Morocco.Journal Article20250810We develop a continuous-time optimal control model for allocating agricultural crop residues between bioenergy production and soil fertility restoration. The system includes a circular reinvestment channel: a portion of the accumulated bioenergy stock is reinvested to enhance soil fertility, thereby closing the loop between energy use and ecological regeneration. The dynamics are governed by a three-state system with a single allocation control. The objective is to maximize a discounted net benefit that accounts for energy revenue, soil value, and operational costs. We apply the Pontryagin Maximum Principle in current-value form to derive necessary optimality conditions and a bang–interior–bang control; no singular arc under our parameterization. Direct optimization confirms a quasi-turnpike phase and shows how the planning horizon and reinvestment efficiency shift switching times and interior duration. The results highlight the strategic role of energy reinvestment in sustainable residue management.https://jmm.guilan.ac.ir/article_9187_f03fea961e8ad67a13da4a93c1b1fdd3.pdfUniversity of GuilanJournal of Mathematical Modeling2345-394X14120260301Improved lower bound of spatial analyticity radius for solutions to nonlinear wave equation347361919210.22124/jmm.2025.30485.2735ENTegegneGetachewDepartment of Mathematics, Mekdela Amba University, EthiopiaBetreShiferawDepartment of Mathematics, Mekdela Amba University, EthiopiaJournal Article20250424In this paper, the rate of decay for the radius of spatial analyticity for solutions of the nonlinear wave equation <br />\[\partial_t^2 u -\Delta u + |u|^{p-1}u=0, \] <br />on $\mathbb{R}^d\times\mathbb{R}$ is studied. In particular, for a<br />class of analytic initial data with a uniform radius of analyticity $\sigma_0$, we obtain an asymptotic lower bound $\sigma(t)\ge a_0|t|^{-\frac23}$ when $d=1$ and $\sigma(t)\ge a_0|t|^{-\frac32}$ when $d=2$ <br />on the uniform radius of analyticity $\sigma(t)$ of solution $u(\cdot,t)$ as $|t|\rightarrow +\infty$ . This is an improvement of the work [D.~O.~da~Silva, A.~J.~Castro, Global well-posedness for the nonlinear wave equation in analytic Gevrey spaces, J. Differential Equations 275(2021)~234--249], where the authors obtained a decay rate of order $\sigma(t)\geq a_0(1+|t|)^{-(\frac{p+1}{2})}$ when $d=1$ and $\sigma(t)\geq a_0(1+|t|)^{-(\frac{p+1-\epsilon}{1-\epsilon})}$ when $d=2$ as $|t|\rightarrow +\infty$ for large time $t$, where $\epsilon>0$ is arbitrary. We used an approximate conservation law in a modified Gevrey space, contraction mapping principle, interpolation and Sobolev embedding to obtain the results.https://jmm.guilan.ac.ir/article_9192_b6c2f551a7382d97222eb8c60a21181b.pdf