IJPAM: Volume 24, No. 3 (2005)

CRITICALITY FOR SOME HYPERBOLIC EQUATIONS

Ali Hakem
Laboratory of Mathematics
University of Sidi-Bel-Abbes
P.O. Box 89, Sidi-Bel-Abbes, 22000, ALGERIA
e-mail: hakemali@yahoo.com


Abstract.We first consider the equation of the following type:

\begin{displaymath} u_{tt}+(-\Delta)^{\frac{\beta}{2}}\ u +g(t)\ u_t= h(t,x)u^{1+p}\,, \end{displaymath} (1)

where $(-\Delta)^{\frac{\beta}{2}}$ is the $\frac{\beta}{2}$-fractional power of the Laplacian $-\Delta$ which, for $0<\beta\leq 2$, stands for impurities, $g(t)$ behaves like $t^{\alpha},\ \alpha>1$. We are interested in nonexistence of globale positive solutions. Then, we consider the criticality for systems of equations of the same type.

Received: July 17, 2005

AMS Subject Classification: 35L60

Key Words and Phrases: blow-up, wave equation, critical exponent

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 24
Issue: 3