Geodesic
The critical case for a semilinear weakly hyperbolic equation
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a22/}
}
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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/