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Brief communications

On unique solvability of one nonlinear nonlocal with respect to a gradient solution of a nonstationary problem

A. S. Ivanova, M. F. Pavlova

Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We consider a parabolic equation whose space operator is a product of nonlinear bounded function which depends on nonlocal characteristic with respect to a solution gradient and strongly monotone, potential operator. We prove the existence and uniqueness of the solution in the class of the vector-valued functions with values in the Sobolev space.

Keywords: parabolic equation, strongly monotone operator, nonlocal operator, generalized solution, solvability, uniqueness.

UDC: 517.63

Received: 26.08.2016

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:3, 67–71

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