Inversion Laplace transform for integrodifferential parabolic equation with purely nonlocal conditions

Abstract

In this paper we prove the existence, uniqueness, and continuous dependence upon the data of solution to integrodifferential parabolic equation with purely nonlocal integral conditions. The proofs are based on a priori estimates and Laplace transform method. Finally, we obtain a solution using a numerical technique which is called Stehfest algorithm by inverting the Laplace transform.