Uniqueness for identifying a space-dependent zeroth-order coefficient in a time-fractional diffusion-wave equation from a single boundary point measurement

Abstract

This paper is focused on a nonlinear inverse problem for identifying a space-dependent zeroth-order coefficient in a time-fractional diffusion-wave equation by the measured data on a single boundary point for one-dimensional case. We give the definition of a weak solution and prove its existence for the corresponding direct problem by using the Fourier method. Based on the Gronwall inequality, analytic continuation and the Laplace transformation, we obtain the uniqueness for the inverse zeroth-order coefficient problem under some simple requirements to the Neumann boundary data.