Asymptotic behavior of solutions to a quasilinear hyperbolic equation with nonlinear damping

We prove the existence and uniqueness of a global solution of a damped quasilinear hyperbolic equation. Key point to our proof is the use of the Yosida approximation. Furthermore, we apply a method based on a specific integral inequality to prove that the solution decays exponentially to zero when t...

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Bibliographic Details
Main Author: M. Aassila
Format: Article
Language:English
Published: University of Szeged 1998-01-01
Series:Electronic Journal of Qualitative Theory of Differential Equations
Online Access:http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=12
Description
Summary:We prove the existence and uniqueness of a global solution of a damped quasilinear hyperbolic equation. Key point to our proof is the use of the Yosida approximation. Furthermore, we apply a method based on a specific integral inequality to prove that the solution decays exponentially to zero when the time t goes to infinity.
ISSN:1417-3875
1417-3875