Geodesic
Blow up of solutions to semilinear wave equations
Electronic Journal of Differential Equations, Tome 2003 (2003).

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

Summary: This work shows the absence of global solutions to the equation $$ u_{tt} = \Delta u + p^{-k}|u|^m,$$ in the Minkowski space $\mathbb{M}_0=\mathbb{R}\times\mathbb{R}^N$, where $ m greater than 1, (N-1)m less than N+1$, and $p $ is a conformal factor approaching 0 at infinity. Using a modification of the method of conformal compactification, we prove that any solution develops a singularity at a finite time.
Classification : 35L70, 35B40, 35L15
Keywords: blow up, conformal compactification 
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     author = {Guedda, Mohammed},
     title = {Blow up of solutions to semilinear wave equations},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a164/}
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Guedda, Mohammed. Blow up of solutions to semilinear wave equations. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a164/