Uniqueness for fractional nonsymmetric diffusion equations and an application to an inverse source problem

Abstract

In this paper, we discuss the uniqueness for solution to time-fractional diffusion equation ${\partial }_t^{\alpha }(u-u_0)+Au=0$ with the homogeneous Dirichlet boundary condition, where an elliptic operator $-A$ is not necessarily symmetric. We prove that the solution is identically zero if its normal derivative with respect to the operator $A$ vanishes on an arbitrary small part of the spatial domain over a time interval. The proof is based on the Laplace transform and the spectral decomposition, and is valid for more general time-fractional partial differential equations, including those involving non symmetric operators.

References in corpus (3)

• Strong maximum principle for fractional diffusion equations and an application to an inverse source problem
• Initial-boundary value problems for fractional diffusion equations with time-dependent coeffcients
• Strong Maximum Principle for Multi-Term Time-Fractional Diffusion Equations and its Application to an Inverse Source Problem