Asymptotic behavior and decay rate estimates for a class of semilinear evolution equations of mixed order |
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Authors: | Hassan Yassine |
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Affiliation: | Université Paul Verlaine - Metz, Laboratoire de Mathématiques et Applications de Metz et CNRS, UMR 7122, Bât. A, Bureau 133, Ile du Saulcy, 57045 Metz Cedex 1, France |
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Abstract: | In this article we present a unified approach to study the asymptotic behavior and the decay rate to a steady state of bounded weak solutions of nonlinear, gradient-like evolution equations of mixed first and second order. The proof of convergence is based on the Lojasiewicz-Simon inequality, the construction of an appropriate Lyapunov functional, and some differential inequalities. Applications are given to nonautonomous semilinear wave and heat equations with dissipative, dynamical boundary conditions, a nonlinear hyperbolic-parabolic partial differential equation, a damped wave equation and some coupled system. |
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Keywords: | primary, 34D05, 34G20, 35B40 secondary, 35M13, 35M33 |
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