Uniqueness for an inverse problem for a nonlinear parabolic system with an integral term by one-point Dirichlet data

被引：3

作者：

Hoemberg, Dietmar ^{[1
,2
]}

Lu, Shuai ^{[3
,4
]}

Yamamoto, Masahiro ^{[5
,6
]}

机构：

[1] Weierstrass Inst Appl Anal & Stochast, Mohrenstr 39, D-10117 Berlin, Germany

[2] NTNU, Dept Math Sci, Alfred Getz Vei 1, N-7491 Trondheim, Norway

[3] Fudan Univ, Key Lab Math Nonlinear Sci, Shanghai 200433, Peoples R China

[4] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[5] Univ Tokyo, Dept Math Sci, Tokyo 1538914, Japan

[6] Peoples Friendship Univ Russia, RUDN Univ, 6 Miklukho Maklaya St, Moscow 117198, Russia

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2019年 / 266卷 / 11期

基金：

日本学术振兴会; 欧盟地平线“2020”;

关键词：

Inverse problems; Uniqueness; Bio-heat equation; Laser thermotherapy; GLOBAL UNIQUENESS; IDENTIFICATION;

D O I：

10.1016/j.jde.2018.12.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider an inverse problem arising in laser-induced thermotherapy, a minimally invasive method for cancer treatment, in which cancer tissues is destroyed by coagulation. For the dosage planning quantitatively reliable numerical simulation are indispensable. To this end the identification of the thermal growth kinetics of the coagulated zone is of crucial importance. Mathematically, this problem is a nonlinear and nonlocal parabolic inverse heat source problem. We show in this paper that the temperature dependent thermal growth parameter can be identified uniquely from a one-point measurement. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：7525 / 7544

页数：20

共 19 条

[1]

Andreucci D., 1992, P ICIAM 1991, P99

[2]

[Anonymous], 1997, FORTSCHRITTE LASERME

[3] Stable determination of a semilinear term in a parabolic equation [J].