University of Guilan Journal of Mathematical Modeling 2345-394X 9 3 2021 09 01 Correctness of the free boundary problem for the microscopic in-situ leaching model 415 423 4549 10.22124/jmm.2021.18402.1581 EN Anvarbek Meirmanov National Research University ``Higher School of Economics'', Moscow, Russia Oleg Galtsev National Research University ``Belgorod State University'', Belgorod, Russia Vladimir Seldemirov National Research University ``Higher School of Economics'', Moscow, Russia Journal Article 2020 12 13 We consider initial boundary value problem for in-situ leaching process of rare metals at the microscopic level. This physical process describes by the Stokes equations for the liquid component coupled with the Lame's equations for the solid skeleton and the diffusion-convection equations for acid concentration. Due to the dissolution of the solid skeleton, the pore space has an unknown (free) boundary. For formulated initial boundary-value problem we prove existence and uniqueness of the classical solution. https://jmm.guilan.ac.ir/article_4549_846531f1451f137cc3acfbba1d8bd47f.pdf