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

摘要

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.

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