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.