Translator Disclaimer
WINTER 2013 Well-posedness and asymptotic behavior of a nonautonomous, semilinear hyperbolic-parabolic equation with dynamical boundary condition of memory type
Hassan Yassine
J. Integral Equations Applications 25(4): 517-555 (WINTER 2013). DOI: 10.1216/JIE-2013-25-4-517

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.

Citation

Download Citation

Hassan Yassine. "Well-posedness and asymptotic behavior of a nonautonomous, semilinear hyperbolic-parabolic equation with dynamical boundary condition of memory type." J. Integral Equations Applications 25 (4) 517 - 555, WINTER 2013. https://doi.org/10.1216/JIE-2013-25-4-517

Information

Published: WINTER 2013
First available in Project Euclid: 31 January 2014

zbMATH: 1286.35042
MathSciNet: MR3161624
Digital Object Identifier: 10.1216/JIE-2013-25-4-517

Subjects:
Primary: 28C15, 28C99, 46E05

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
39 PAGES


SHARE
Vol.25 • No. 4 • WINTER 2013
Back to Top