Cauchy problem for a nonlinear viscoelastic equation with nonlinear damping and source terms. (English) Zbl 1218.35128
Summary: We consider a Cauchy problem for a nonlinear viscoelastic equation with nonlinear damping and source terms. Under suitable assumptions on the initial data and the relaxation function, we establish a finite-time blow-up result and a global existence result.
MSC:
| 35L15 | Initial value problems for second-order hyperbolic equations |
| 35L71 | Second-order semilinear hyperbolic equations |
| 35R09 | Integro-partial differential equations |
| 35B44 | Blow-up in context of PDEs |
Keywords:
nonlinear viscoelastic equation; global existence; blow up; relaxation function; global existenceReferences:
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