A nonlinear parabolic integro-differential problem with an unknown Dirichlet boundary condition

被引：5

作者：

Grimmonprez, Marijke ^{[1
]}

Slodicka, Marian ^{[1
]}

机构：

[1] Univ Ghent, Dept Math Anal, B-9000 Ghent, Belgium

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2015年 / 275卷

关键词：

Nonlinear parabolic equation; Unknown Dirichlet condition; NONLOCAL BOUNDARY; EQUATION;

D O I：

10.1016/j.cam.2014.04.022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A nonlinear parabolic integro-differential equation partial derivative(t)g(u) - Delta u = F + integral(t)(0) f(s, u(s)) ds with a known Neumann boundary condition on a part of the boundary and an unknown Dirichlet boundary condition alpha(t) on the other part of the boundary is studied. The inverse problem of identifying the unknown time-dependent function alpha(t) from an additional integral measurement E(t) = integral(Omega) g(u(t, x)) dx is investigated. The well-posedness of the problem in suitable function spaces is shown and a numerical time-discrete scheme for approximations is designed. Convergence of the proposed scheme is supported by a numerical experiment. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：421 / 432

页数：12

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