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

In this article, we discuss a solution to time‐fractional diffusion equation ∂tα(u−u0)+Au=0$$ {\partial}_t^{\alpha}\left(u-{u}_0\right)+ Au=0 $$ with the homogeneous Dirichlet boundary condition, where an elliptic operator −A$$ -A $$ is not necessarily symmetric. We prove that the solution u$$ u $$ is identically zero if its normal derivative with respect to the operator A$$ A $$ 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. [ABSTRACT FROM AUTHOR]