This paper deals with an inverse problem of identifying a space dependent coefficient
in a time-fractional diffusion equation on a finite domain with final observation. The
existence and uniqueness of this inverse problem are proved. A numerical scheme is
proposed to solve the problem. The main idea of the proposed scheme is approximating
the time fractional derivative by Diethelm’s quadrature formula and use the local
discontinuous Galerkin method in space variable. Also, an error estimate for this
problem is presented. Finally, two numerical example is studied to demonstrate the
accuracy and efficiency of the proposed method.
کلید واژگان :
Inverse problem · Existence and uniqueness · Local discontinuous Galerkin method · Error estimate · Riemann–Liouville derivative
