A new approach for determination of boundary function for diffusion equation by fourier method

Abstract

We consider a linear diffusion equation with a nonlocal boundary condition. We attempt to recover the boundary condition and the solution of diffusion equation for a problem by making use of an over-determination condition of integral type. Explicit solutions for these unknowns are derived by employing Fourier method. We obtain sufficient conditions for the existence and uniqueness of the solution and determination of boundary condition.