A simultaneous approach to inverse source problem by Green's function

Erdem A.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.38, no.7, pp.1393-1404, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 7
  • Publication Date: 2015
  • Doi Number: 10.1002/mma.3154
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1393-1404
  • Kocaeli University Affiliated: Yes

Abstract

In this paper, we consider an inverse source problem of identification of F(t) function in the linear parabolic equation u(t)=u(xx)+F(t) and u(0)(x) function as the initial condition from the measured final data and local boundary data. Based on the optimal control framework by Green's function, we construct Frechet derivative of Tikhonov functional. The stability of the minimizer is established from the necessary condition. The CG algorithm based on the Frechet derivative is applied to the inverse problem, and results are presented for a test example. Copyright (c) 2014 John Wiley & Sons, Ltd.