Inverse source problem for a one-dimensional time-fractional diffusion equation and unique continuation for weak solutions

Abstract

In this paper, we obtain the sharp uniqueness for an inverse $x$-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data. The key ingredient is the unique continuation which holds for weak solutions.

24 pages

References in corpus (2)

• Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
• Classical unique continuation property for multi-terms time fractional diffusion equations

Cited by in corpus (2)

• Well-posedness of the stochastic time-fractional diffusion and wave equations and inverse random source problems
• Uniqueness of inverse source problems for time-fractional diffusion equations with singular functions in time