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

作者：Jiang, Daijun; Li, Zhiyuan^*; Pauron, Matthieu; Yamamoto, Masahiro

来源：MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46(2): 2275-2287.

DOI：10.1002/mma.8644

• fractional partial differential equations
• inverse problems
• unique continuation

In this article, we discuss a solution to time-fractional diffusion equation partial differential partial derivative(alpha)(t)(u-u0)+Au=0 with the homogeneous Dirichlet boundary condition, where an elliptic operator -A is not necessarily symmetric. We prove that the solution u is identically zero if its normal derivative with respect to the operator A vanishes on an arbitrarily chosen subboundary of the spatial domain over a time interval. The proof is based on the Laplace transform and the spectral decomposition for a nonsymmetric elliptic operator. As a direct application, we prove the uniqueness result for an inverse problem on determining the spatial component in the source term by Neumann boundary data on subdoundary.