On solvability of a elliptic-parabolic problem of nonlinear filtration theory

11th International Conference on "Mesh methods for boundary-value problems and applications"

Pavlova, M.F.^1 ; Rung, E.V.^2

Department of Computational Mathematics, Institute of Computational Mathematics and Information Technologies, Kazan Federal University, 18 Kremlyovskaya Street, Kazan

420008, Russia^1

Department of Applied Mathematics, Institute of Computational Mathematics and Information Technologies, Kazan Federal University, 18 Kremlyovskaya Street, Kazan

420008, Russia^2

关键词: Existence theorem;    Generalized solution;    Initial-boundary value problems;    Kirchhoff;    Nonlinear filtration;    Parabolic problems;    Semidiscretization;    Strong solution;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012076/pdf
DOI  :  10.1088/1757-899X/158/1/012076

来源: IOP

【 摘 要 】

Existence of a strong solution of the initial-boundary value problem modeling the process of liquid filtration in an arbitrary bounded region Ω of space Rnis proven. For determining a generalized solution, the Kirchhoff transform is used, and it is assumed that the domain of the Kirchhoff function constitutes only a part of the real axis. For proving the existence theorem, the method of semidiscretization with respect to the variable t and the Galerkin method are used.