On the blow up of solutions for hyperbolic equation involving the fractional Laplacian with source terms

In this paper, we study the blow-up of solutions for hyperbolic equations involving the fractional Laplacian operator with damping and source terms.  We obtain the global existence results. Then, we observe the blow-up of solutions using the concavity method. Finally, we present some numerical simulation results.

Keywords:

Blow up , energy function , hyperbolic equation , fractional Laplacian , source terms , fractional Sobolev spaces