Local Existence and Blow-Up of Solutions for Wave Equation Involving the Fractional Laplacian with Nonlinear Source Term

Abstract

The aim of this paper is to investigate the local weak existence and vacuum isolating of solutions, asymptotic behavior, and blow-up of the solutions for a wave equation involving the fractional Laplacian with nonlinear source. By means of the Galerkin approximations, we prove the local weak existence and finite time blow-up of the solutions and we give the upper and lower bounds for blow-up time.

Keywords

• fractional derivatives
• existence
• fractional Laplacian
• local solution
• blow-up