IJPAM: Volume 76, No. 4 (2012)

GLOBAL EXISTENCE, EXPONENTIAL AND POLYNOMIAL
DECAY SOLUTIONS FOR A SYSTEM CLASS OF
NONLINEAR HIGHER-ORDER WAVE EQUATIONS
WITH DAMPING AND SOURCE TERMS

Erhan Pişkin$^1$, Necat Polat$^2$
$^{1,2}$Department of Mathematics
Dicle University
Diyarbakir, TURKEY


Abstract. We consider the system a class of nonlinear higher-order wave equations \begin{equation*} \left\{ \begin{array}{c} u_{tt}+\left( -\bigtriangleup \ri... ... ^{q-1}v_{t}=f_{2}\left( u,v\right) ,\ \end{array}% \right. \end{equation*}
with initial and Dirichlet boundary conditions. Under suitable conditions on the initial datum, the theorems of global existence and decay are proved.

Received: January 17, 2012

AMS Subject Classification: 35B40, 35G31

Key Words and Phrases: decay, higher-order wave equations, nonlinear damping and source terms

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 76
Issue: 4