Global existence and blowup of solutions to a class of wave equations with Hartree type nonlinearity

Abstract

Abstract In this paper, we consider a class of wave-Hartree equations on a bounded smooth convex domain with Dirichlet boundary condition. We prove the local existence of solutions in the natural energy space by using the standard Galërkin method. The results on global existence and nonexistence of solutions are obtained mainly by means of the potential well theory and concavity method.