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

Erdem A.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.38, sa.7, ss.1393-1404, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 7
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1002/mma.3154
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1393-1404
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.