An inverse time-fractional diffusion problem with Robin boundary condition in two layers spherical domain

In this paper, I am interested in the study of the inverse Cauchy boundary value problem for the time-fractional diffusion equation in two layers spherical domain. Given the data in the first layer, my goal is to recover the temperature distribution and the heat flux in the second layer. First, I pr...

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Bibliographic Details
Published inComputational & applied mathematics Vol. 40; no. 8
Main Author Luan, Tran Nhat
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2021
Springer Nature B.V
Subjects
Applications of Mathematics
Applied physics
Boundary conditions
Boundary value problems
Computational mathematics
Computational Mathematics and Numerical Analysis
Diffusion layers
Domains
Exact solutions
Heat flux
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Regularization
Temperature distribution
Robin boundary condition
Fourier truncated method
30A10
26A33
Ill-posed problem
Time-fractional diffusion equation
35R25
47J06
Composite material
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Summary:In this paper, I am interested in the study of the inverse Cauchy boundary value problem for the time-fractional diffusion equation in two layers spherical domain. Given the data in the first layer, my goal is to recover the temperature distribution and the heat flux in the second layer. First, I prove that the problem is severely ill-posed in the Hadamard sense. After, I propose a truncation-type regularization approach enabling us to achieve Hölder-type error in L 2 -norm between the regularized and exact solutions.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-021-01685-2