The enclosure method for the detection of variable order in fractional diffusion equations
| Autor: | Masaru Ikehata, Yavar Kian |
|---|---|
| Přispěvatelé: | Hiroshima University, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), CPT - E8 Dynamique quantique et analyse spectrale, Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), ANR-17-CE40-0029,MultiOnde,Problèmes Inverses Multi-Onde(2017) |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
Control and Optimization
space-dependent variable order Mathematics - Analysis of PDEs 35R30 35L05 anomalous diffusion Modeling and Simulation FOS: Mathematics Discrete Mathematics and Combinatorics inverse problem [MATH]Mathematics [math] time-fractional diffusion equation Analysis Analysis of PDEs (math.AP) enclosure method |
| Zdroj: | Inverse Problems and Imaging Inverse Problems and Imaging, 2023, 17 (1), pp.180-202. ⟨10.3934/ipi.2022036⟩ |
| ISSN: | 1930-8337 1930-8345 |
| DOI: | 10.3934/ipi.2022036⟩ |
| Popis: | International audience; This paper is concerned with a new type of inverse obstacle problem governed by a variable-order time-fraction diffusion equation in a bounded domain. The unknown obstacle is a region where the space dependent variable-order of fractional time derivative of the governing equation deviates from a known homogeneous background one. The observation data is given by the Neumann data of the solution of the governing equation for a specially designed Dirichlet data. Under a suitable jump condition on the deviation, it is shown that the most recent version of the time domain enclosure method enables one to extract information about the geometry of the obstacle and a qualitative nature of the jump, from the observation data. |
| Databáze: | OpenAIRE |
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