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Determining functionals for damped nonlinear wave equations. (English) Zbl 1394.35039

Summary: The paper is devoted to the study of asymptotic behavior as \(t\to +\infty\) of solutions of initial boundary value problem for strongly damped nonlinear wave equation and strongly damped Kirchhoff type equation under homogeneous Dirichlet’s boundary conditions. We proved that the asymptotic behavior as \(t\to\infty\) of solutions of these problem is completely determined by dynamics of finitely many functionals.

MSC:

35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
35B35 Stability in context of PDEs
35L20 Initial-boundary value problems for second-order hyperbolic equations
35L70 Second-order nonlinear hyperbolic equations
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