Geodesic
The critical case for a semilinear weakly hyperbolic equation
Electronic journal of differential equations, Tome 2004 (2004)
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 $t_0$ 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.
Classification : 35L70, 35L15, 35L80
Keywords: global existence, semilinear wave equations 
@article{EJDE_2004__2004__a22,
     author = {Fanelli,  Luca and Lucente,  Sandra},
     title = {The critical case for a semilinear weakly hyperbolic equation},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1072.35556},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a22/}
}
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AU  - Lucente,  Sandra
TI  - The critical case for a semilinear weakly hyperbolic equation
JO  - Electronic journal of differential equations
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%A Lucente,  Sandra
%T The critical case for a semilinear weakly hyperbolic equation
%J Electronic journal of differential equations
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%F EJDE_2004__2004__a22
Fanelli,  Luca; Lucente,  Sandra. The critical case for a semilinear weakly hyperbolic equation. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a22/