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Dynamics around the ground state of a nonlinear evolution equation. (English) Zbl 1159.35390

Summary: We analyze the qualitative behavior of solutions forwards and backwards. We present characterizations of blowup, boundedness and convergence to the ground state as \(t\rightarrow \pm \infty \). We define and use a potential well and several invariant and positive invariant sets.

MSC:

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