The dynamics of a nonlinear wave equation. (English) Zbl 1015.35072

Author’s abstract: We consider a wave equation in a bounded domain with linear dissipation and with a nonlinear source term. We give characterizations of all the solutions with respect to their qualitative properties: globality, boundedness, nonglobality, blow-up and convergence to equilibria.


35L70 Second-order nonlinear hyperbolic equations
35L20 Initial-boundary value problems for second-order hyperbolic equations
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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