Local Existence and Blow-Up of Solutions for Wave Equation Involving the Fractional Laplacian with Nonlinear Source Term - Younes Bidi; Abderrahmane Beniani; Keltoum Bouhali; Khaled Zennir; Hatim M. ElKhair; Eltegani I. Hassan; Almonther Alarfaj (Axioms, 2023)
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.