Blow up of solutions to semilinear wave equations
| Autor: | Mohammed Guedda |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2003 |
| Předmět: | |
| Zdroj: | Electronic Journal of Differential Equations, Vol 2003, Iss 53, Pp 1-5 (2003) |
| Druh dokumentu: | article |
| ISSN: | 1072-6691 |
| Popis: | This work shows the absence of global solutions to the equation $$ u_{tt} = Delta u + p^{-k}|u|^m, $$ in the Minkowski space $mathbb{M}_0=mathbb{R}imesmathbb{R}^N$, where $ m > 1$, $(N-1)m < N+1$, 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. |
| Databáze: | Directory of Open Access Journals |
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