Unique determination of fractional order and source term in a fractional diffusion equation from sparse boundary data

Abstract

In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system corresponding to our diffusion equation, we construct useful quantitative relation between unknowns and measurements. From Laplace transform and the knowledge in complex analysis, the uniqueness theorem is proved.

References in corpus (10)

• A Tutorial on Inverse Problems for Anomalous Diffusion Processes
• Geometrical structure of Laplacian eigenfunctions
• Physical Pictures of Transport in Heterogeneous Media: Advection-Dispersion, Random Walk and Fractional Derivative Formulations
• Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins
• Strong maximum principle for fractional diffusion equations and an application to an inverse source problem
• Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations
• Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation
• Uniqueness in inverse boundary value problems for fractional diffusion equations
• Recovering an Unknown Source in a Fractional Diffusion Problem
• Reconstruction of the Temporal Component in the Source Term of a (Time-Fractional) Diffusion Equation

Cited by in corpus (4)

• Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior
• Theoretical and numerical studies of inverse source problem for the linear parabolic equation with sparse boundary measurements
• Well-posedness of the stochastic time-fractional diffusion and wave equations and inverse random source problems
• Recovering Multiple Fractional Orders in Time-Fractional Diffusion in an Unknown Medium