Geodesic
Study of some mathematical models for nonstationary filtration processes
Numerical methods and programming, Tome 21 (2020) no. 1, pp. 1-12.

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We consider some mathematical models connected with the study of nonstationary filtration processes in underground hydrodynamics. These models involve nonlinear problems for parabolic equations with unknown source functions. One of the problems is a system consisting of a boundary value problem of the first kind and an equation describing a time dependence of the sought source function. In the other problem, the corresponding system is distinguished from the first one by boundary conditions of the second kind. These problems essentially differ from usual boundary value problems for parabolic equations. The aim of our study is to establish conditions of unique solvability in a class of smooth functions for the considered nonlinear parabolic problems. The proposed approach involves the proof of a priori estimates for the Rothe method.
Mots-clés : parabolic equations, filtration processes.
Keywords: boundary value problems, Holder spaces, Rothe method 
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N. L. Gol'dman. Study of some mathematical models for nonstationary filtration processes. Numerical methods and programming, Tome 21 (2020) no. 1, pp. 1-12. http://geodesic.mathdoc.fr/item/VMP_2020_21_1_a0/