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

共 50 条

[31] Existence of solution to a nonlocal biharmonic problem with dependence on gradient and Laplacian
Shilpa
Dwivedi, Gaurav
JOURNAL OF APPLIED ANALYSIS, 2022, 28 (02) : 211 - 218
[32] ON ONE SOLUTION OF A NONLOCAL BOUNDARY VALUE PROBLEM FOR A NONLINEAR PARTIAL DIFFERENTIAL EQUATION OF THE THIRD ORDER
Manat, A. M.
Orumbayeva, N. T.
JOURNAL OF MATHEMATICS MECHANICS AND COMPUTER SCIENCE, 2024, 121 (01): : 65 - 75
[33] UNIQUE SOLUTION FOR ONE PROBLEM OF OPTIMAL CONTROL
ZENISEK, V
INTERNATIONAL JOURNAL OF CONTROL, 1973, 17 (04) : 775 - 784
[34] On the unique solvability of a nonlocal boundary value problem with data on intersecting lines for systems of hyperbolic equations
A. T. Asanova
Differential Equations, 2009, 45 : 385 - 394
[35] On the unique solvability of a nonlocal boundary value problem with data on intersecting lines for systems of hyperbolic equations
Assanova, A. T.
DIFFERENTIAL EQUATIONS, 2009, 45 (03) : 385 - 394
[36] NUMERICAL SOLUTION OF ONE NONHOMOGENEOUS NONLOCAL MIXED PROBLEM
Aliyev, Aydin Y.
PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2005, 22 (30): : 179 - 186
[37] Unique Solvability of a Two-Dimensional Nonstationary Problem for the Convection Equations with Temperature-Dependent Viscosity
O. N. Goncharova
Differential Equations, 2002, 38 : 249 - 258
[38] Unique solvability of a two-dimensional nonstationary problem for the convection equations with temperature-dependent viscosity
Goncharova, ON
DIFFERENTIAL EQUATIONS, 2002, 38 (02) : 249 - 258
[39] On the Unique Solvability of the Problem of the Flow of an Aqueous Solution of Polymers near a Critical Point
A. G. Petrova
Mathematical Notes, 2019, 106 : 784 - 793
[40] On the Unique Solvability of the Problem of the Flow of an Aqueous Solution of Polymers near a Critical Point
Petrova, A. G.
MATHEMATICAL NOTES, 2019, 106 (5-6) : 784 - 793

← 1 2 3 4 5 →