The enclosure method for the detection of variable order in fractional diffusion equations

2022/02/06 by Masaru Ikehata, Yavar Kian, Ikehata, Masaru +1 · 1 citation
Mathematics · #35L05 #35R30 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical methods in inverse problems #math.AP #msc:35L05 #msc:35R30

paper · pdf · doi:10.48550/arxiv.2202.02726

openalex publication_date 2022/02/06 · arxiv created 2022/02/17 · arxiv updated 2022/02/18 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Unique and Stable Recovery of Space-Variable Order in Multidimensional Subdiffusion

Related

• Recovery of the Order of Derivation for Fractional Diffusion Equations in an Unknown Medium
• Uniqueness in determination of the fractional order in the TFDE using one measurement
• Uniqueness of determining the variable fractional order in variable-order time-fractional diffusion equations
• Inverse source problem with a posteriori boundary measurement for fractional diffusion equations
• Unique determination of several coefficients in a fractional diffusion(-wave) equation by a single measurement