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On coupled nonlinear wave equations of Kirchhoff type with damping and source terms. (English) Zbl 1203.35165

Summary: The initial boundary value problem for a system of nonlinear wave equations of Kirchhoff type with strong damping in a bounded domain is considered. The existence, asymptotic behavior and blow-up of solutions are discussed under some conditions. The decay estimates of the energy function and the estimates for the lifespan of solutions are given.

MSC:

35L53 Initial-boundary value problems for second-order hyperbolic systems
35L72 Second-order quasilinear hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
35R09 Integro-partial differential equations
35B44 Blow-up in context of PDEs
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