Electron. J. Diff. Eqns., Vol. 2002(2002), No. 91, pp. 1-22.

Existence of global solutions to a quasilinear wave equation with general nonlinear damping

Mohammed Aassila & Abbes Benaissa

In this paper we prove the existence of a global solution and study its decay for the solutions to a quasilinear wave equation with a general nonlinear dissipative term by constructing a stable set in $H^{2}\cap H_{0}^{1}$.

Submitted July 02, 2002. Published October 26, 2002.
Math Subject Classifications: 35B40, 35L70, 35B37.
Key Words: Quasilinear wave equation, global existence, asymptotic behavior, nonlinear dissipative term, multiplier method.

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Mohammed Aassila
Mathematisches Institut
Universitat zu Koln
Weyertal 86-90, D-50931 Koln, Germany.
e-mail: aassila@mi.uni-koeln.de
Abbes Benaissa
Universite Djillali Liabes
Faculte des Sciences
D\'epartement de Math\'ematiques
B. P. 89, Sidi Bel Abbes 22000, Algeria
e-mail: benaissa_abbes@yahoo.com

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