Existence, blow up and growth of solutions for a coupled quasi-linear viscoelastic Petrovsky equations with degenerate damping terms

Abstract

We consider a quasi-linear coupled system of two viscoelastic equations with degenerate damping and source terms under the Dirichlet boundary condition. We obtain the global existence, blow up and exponential growth of solutions under some restrictions on the initial data, relaxation functions and degenerate damping terms.

Subject Classification: (2010):

• 35B44
• 35L05
• 35L75

Keywords:

• Petrovsky equations
• Viscoelastic equations
• Degenerate damping
• Quasilinear equations