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

被引：1

作者：

Ivanova A.S. ^{[1
]}

Pavlova M.F. ^{[1
]}

机构：

[1] Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan

来源：

Russian Mathematics | 2017年 / 61卷 / 3期

关键词：

generalized solution; nonlocal operator; parabolic equation; solvability; strongly monotone operator; uniqueness;

D O I：

10.3103/S1066369X17030082

中图分类号：

学科分类号：

摘要：

We consider a parabolic equation whose space operator is a product of a nonlinear bounded function which depends on a nonlocal characteristic with respect to a solution gradient and a 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. © 2017, Allerton Press, Inc.

引用

页码：67 / 71

页数：4

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