Distinguishability of a source function in a time fractional inhomogeneous parabolic equation with Robin boundary condition

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Ozbilge E., DEMİR A.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.47, no.6, pp.1503-1511, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 6
  • Publication Date: 2018
  • Doi Number: 10.15672/hjms.20164517213
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1503-1511
  • Keywords: Inverse problem, time-fractional parabolic equation, distinguishability, INVERSE PROBLEM, DIFFUSION, IDENTIFICATION, APPROXIMATION
  • Kocaeli University Affiliated: Yes

Abstract

This article deals with the mathematical analysis of the inverse problem of identifying the distinguishability of input-output mappings in the linear time fractional inhomogeneous parabolic equation D(t)(alpha)u(x, t) = (k(x)u(x))(x) + F(x, t) 0 < alpha <= 1, with Robin boundary conditions u(0, t) = psi(0)(t), u(x)(1,t ) = gamma(u(1, t) - psi(1)(t)). By defining the input-output mappings Phi[.] : K -> C-1[0, T] and Psi[.] : K -> C[0, T] the inverse problem is reduced to the problem of their invertibility. Hence, the main purpose of this study is to investigate the distinguishability of the input-output mappings Phi[.] and Psi[.]. Moreover, the measured output data f(t) and h(t) can be determined analytically by a series representation, which implies that the input-output mappings Phi[.] : K -> C-1[0, T] and Psi[.] : K -> C[0, T] can be described explicitly.