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 (1)

• Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins

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