INVERSE PROBLEMS FOR THE HEAT EQUATION WITH MEMORY

被引：12

作者：

Avdonin, Sergei A. ^{[1
]}

Ivanov, Sergei A. ^{[2
]}

Wang, Jun-Min ^{[3
]}

机构：

[1] Univ Alaska Fairbanks, Fairbanks, AK 99775 USA

[2] Russian Acad Sci, Mendeleev Line 1, St Petersburg, Russia

[3] Beijing Inst Technol, Beijing 100081, Peoples R China

来源：

INVERSE PROBLEMS AND IMAGING | 2019年 / 13卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Gurtin-Pipkin equation; inverse problem; Borg-Marchenko theorem; IDENTIFICATION;

D O I：

10.3934/ipi.2019002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study inverse boundary problems for one dimensional linear integro-differential equation of the Gurtin-Pipkin type with the Dirichlet-to-Neumann map as the inverse data. Under natural conditions on the kernel of the integral operator, we give the explicit formula for the solution of the problem with the observation on the semiaxis t > 0. For the observation on finite time interval, we prove the uniqueness result, which is similar to the local Borg-Marchenko theorem for the Schrodinger equation.

引用

页码：31 / 38

页数：8

共 19 条

[1] BOUNDARY CONTROL AND A MATRIX INVERSE PROBLEM FOR THE EQUATION U(TT)-U(XX)+V(X)U=O [J].