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On the solvability of the problem of the coupled movement of underground and surface waters with nonhomogeneous bounds to the solution

L. L. Glazyrina, M. F. Pavlova

Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University

Abstract: We consider the problem that belongs to the class of problems with double degeneration. The main characteristic of this problem is a nonlocal boundary condition on the slit of the domain. By using the semidiscretization and penalty methods the theorem of the solvability of the first boundary condition problem for the corresponding variational inequality with nonhomogeneous bounds to the solution is proved.

Keywords: double degeneration, nonlocal boundary conditions, semidiscretization method, penalty method, generalized solution.

UDC: 519.6

Received: 20.11.2011