This article is cited in 7 papers

Brief communications

The unique solvability of a certain nonlocal nonlinear problem with a spatial operator strongly monotone with respect to the gradient

O. V. Glyzarina, M. F. Pavlova

Chair of Computational Mathematics, Kazan (Volga Region) Federal University, Kazan, Russia

Abstract: We consider a nonlinear degenerate parabolic equation whose spatial operator depends on a nonlocal characteristic of the solution. We prove the uniqueness of the solution in the class of vector-valued functions that take on values in Sobolev spaces.

Keywords: parabolic equation, monotone operator, nonlocal operator, uniqueness.

UDC: 517.63

Presented by the member of Editorial Board: R. Z. Dautov
Received: 22.09.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:3, 83–86

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