On the asymptotic behavior of inverse problems for parabolic equation

被引：0

作者：

Lemeshkova, Elena ^{[1
]}

Andreev, Viktor ^{[1
]}

机构：

[1] ICM SB RAS, Krasnoyarsk, Russia

来源：

JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS | 2021年 / 7卷 / 02期

关键词：

Parabolic equation; Inverse problem; A priori estimates; Asymptotic behavior;

D O I：

10.1007/s41808-021-00127-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study two inverse initial-boundary value problems for a linear parabolic equation. These equations arise in mathematical modeling of the viscous heat-conducting fluid motion with two or one free boundaries. The unknown function of time enters the right-hand side of the equation additively and is found from the additional condition of integral overdetermination. For both problems, a priori estimates of solutions in the uniform metric are obtained. Stationary solutions are found. Sufficient conditions for the input data, under which the solutions with increasing time tend to the stationary regime according to the exponential law, are established.

引用

页码：905 / 921

页数：17

共 50 条

[1] On the asymptotic behavior of inverse problems for parabolic equation
Elena Lemeshkova
Viktor Andreev
Journal of Elliptic and Parabolic Equations, 2021, 7 : 905 - 921
[2] On the asymptotic behavior of solutions to inverse problems for parabolic equations
I. A. Vasin
V. L. Kamynin
Siberian Mathematical Journal, 1997, 38 : 647 - 662
[3] On the asymptotic behavior of solutions to inverse problems for parabolic equations
Vasin, IA
Kamynin, VL
SIBERIAN MATHEMATICAL JOURNAL, 1997, 38 (04) : 647 - 662
[4] An asymptotic expansion of the fundamental solution for a parabolic equation and inverse problems
V. G. Romanov
Doklady Mathematics, 2015, 92 : 541 - 544
[5] An asymptotic expansion of the fundamental solution for a parabolic equation and inverse problems
Romanov, V. G.
DOKLADY MATHEMATICS, 2015, 92 (02) : 541 - 544
[6] Asymptotic Behavior of Solutions of Inverse Problems for Degenerate Parabolic Equations
V. L. Kamynin
Differential Equations, 2018, 54 : 633 - 647
[7] Asymptotic Behavior of Solutions of Inverse Problems for Degenerate Parabolic Equations
Kamynin, V. L.
DIFFERENTIAL EQUATIONS, 2018, 54 (05) : 633 - 647
[8] INVERSE PROBLEMS FOR A QUASILINEAR PARABOLIC EQUATION
KLIBANOV, MV
DOKLADY AKADEMII NAUK SSSR, 1979, 245 (03): : 530 - 532
[9] COMPACTLY SUPPORTED STATIONARY PROBLEMS AND ASYMPTOTIC-BEHAVIOR OF A DEGENERATE PARABOLIC EQUATION
SCHATZMAN, M
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1982, 294 (02): : 83 - 85
[10] Asymptotic behavior of solutions of some inverse problems for higher-order parabolic equations
Kamynin, V
Francini, E
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 1999, 6 (04) : 394 - 408

← 1 2 3 4 5 →