IJPAM: Volume 31, No. 2 (2006)

ON EXACT SOLUTIONS OF
A QUASILINEAR WAVE EQUATION WITH SOURCE TERM

Nour-Eddine Amroun$^1$, Abbès Benaissa$^2$
$^{1,2}$Laboratory of Mathematics
Djillali Liabès University
P.O. Box 89, Sidi Bel Abbès, 22000, ALGERIA
$^1$e-mail: amroun$_{-}$nour@yahoo.com
$^2$e-mail: benaissa$_{-}$abbes@yahoo.com


Abstract.In this paper, we construct exact solutions of the Cauchy problem of degenerate quasilinear wave equation of Kirchhoff type. We observe the effect of the nonlinear terms on the existence of solutions. We construct solutions which exist globally for some initial data, or blow up in a finite time for other initial data. 35C05, 35L70

Received: July 18, 2006

AMS Subject Classification: 35C05, 35L70

Key Words and Phrases: Kirchhoff equation, exact solutions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 31
Issue: 2