Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 101, pp. 1-13.

Title: The critical case for a semilinear weakly hyperbolic equation

Authors: Luca Fanelli (Univ. "La Sapienza" di Roma, Italy)
         Sandra Lucente (Univ. degli Studi di Bari, Italy)
 
Abstract: 
 We prove a global existence result for the Cauchy problem, in the
 three-dimensional space,  associated with the equation
 $$
 u_{tt}-a_\lambda(t) \Delta_x u=-u|u|^{p(\lambda)-1}
 $$
 where $a_\lambda(t)\ge 0$ and behaves as $(t-t_0)^\lambda$ close
 to some $t_0>0$ with $a(t_0)=0$, and
 $p(\lambda)=(3\lambda+10)/(3\lambda+2)$ with $3\le p(\lambda)\le 5$.
 This means that we deal with the superconformal, critical
 nonlinear case. Moreover we assume a small initial energy.
 
Submitted July 22, 2004. Published August 24, 2004.
Math Subject Classifications: 35L70, 35L15, 35L80.
Key Words: Global existence; semilinear wave equations.