Geodesic
Blow up of solutions to semilinear wave equations
Electronic journal of differential equations, Tome 2003 (2003)
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 
@article{EJDE_2003__2003__a164,
     author = {Guedda,  Mohammed},
     title = {Blow up of solutions to semilinear wave equations},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1032.35137},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a164/}
}
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TI  - Blow up of solutions to semilinear wave equations
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VL  - 2003
UR  - http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a164/
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ID  - EJDE_2003__2003__a164
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%A Guedda,  Mohammed
%T Blow up of solutions to semilinear wave equations
%J Electronic journal of differential equations
%D 2003
%V 2003
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%F EJDE_2003__2003__a164
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/