Inverse Problem for an Equation with A Nonstandard Growth Condition

被引：4

作者：

Antontsev, S. N. ^{[1
]}

Aitzhanov, S. E. ^{[2
]}

机构：

[1] Russian Acad Sci, Lavrentev Inst Hydrodynam, Siberian Branch, Novosibirsk 630090, Russia

[2] Al Farabi Kazakh Natl Univ, Alma Ata 050038, Kazakhstan

来源：

JOURNAL OF APPLIED MECHANICS AND TECHNICAL PHYSICS | 2019年 / 60卷 / 02期

关键词：

inverse problem; integral overdetermination condition; parabolic equations with a nonstandard growth condition; solvability; blow-up of the solution; asymptotic solution behavior;

D O I：

10.1134/S0021894419020081

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

This paper describes an inverse problem for determining the right side of a parabolic equation with a nonstandard growth condition and integral overdetermination condition. The Galerkin method is used to prove the existence of two solutions of the inverse problem and their uniqueness, one of them being local and the other one being global in time. Sufficient blow-up conditions for the local solution for a finite time in a limited region with a homogeneous Dirichlet condition on its boundary are obtained. The blow-up of the solution is proven using the Kaplan method. The asymptotic behavior of the inverse problem solutions for large time values is investigated. Sufficient conditions for vanishing of the solution for a finite time are obtained. Boundary conditions ensuring the corresponding behavior of the solutions are considered.

引用

页码：265 / 277

页数：13

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