Study of some mathematical models for nonstationary filtration processes




parabolic equations, boundary value problems, Holder spaces, Rothe method, filtration processes


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.

Author Biography

N.L. Gol’dman

Lomonosov Moscow State University,
Research Computing Center
Leninskie Gory, Moscow, 119991, Russia
• Leading Researcher


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How to Cite

Гольдман Н.Л. Study of Some Mathematical Models for Nonstationary Filtration Processes // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2020. 21. 1-12. doi 10.26089/NumMet.v21r101



Section 1. Numerical methods and applications

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