Global solutions of a fractional semilinear pseudo-parabolic equation with nonlocal source

Abstract

In this paper, the initial boundary value problem for a fractional nonlocal semilinear pseudo-parabolic equation is established. Firstly, we get the local solution by the standard Galerkin method and the priori estimates. Next, by applying potential well argument, the existence and uniqueness of the global solution are proved for initial energy .