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- W2024176044 abstract "We consider a nonautonomous, semilinear, hyperbolic-parabolic equation subject to a dynamical boundary condition of memory type. First we prove the existence and uniqueness of global bounded solutions having relatively compact range in the natural energy space. Under the assumption that the nonlinear term $f$ is real analytic, we then derive an appropriate Lyapunov energy and we use the {L}ojasiewicz-Simon inequality to show the convergence of global weak solutions to single steady states as time tends to infinity. Finally, we provide an estimate for the convergence rate." @default.
- W2024176044 created "2016-06-24" @default.
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- W2024176044 date "2013-12-01" @default.
- W2024176044 modified "2023-09-27" @default.
- W2024176044 title "Well-posedness and asymptotic behavior of a nonautonomous, semilinear hyperbolic-parabolic equation with dynamical boundary condition of memory type" @default.
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- W2024176044 doi "https://doi.org/10.1216/jie-2013-25-4-517" @default.
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