University of Guilan Journal of Mathematical Modeling 2345-394X 14 1 2026 03 01 A theoretical study for air pollution model as‎ a free boundary ‎problem‎ 115 135 9093 10.22124/jmm.2025.29478.2618 EN Karim Ivaz Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran Gader Darkhoshi Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran Journal Article 2025 01 05 This 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 equation https://jmm.guilan.ac.ir/article_9093_8749466cf63127b26ef7695bf67d0b4f.pdf