Blow up of solutions to semilinear wave equations
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 c...
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| Format: | Article |
| Language: | English |
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Texas State University
2003-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2003/53/abstr.html |
| _version_ | 1818163060170293248 |
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| author | Mohammed Guedda |
| author_facet | Mohammed Guedda |
| author_sort | Mohammed Guedda |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T16:43:33Z |
| format | Article |
| id | doaj.art-56f38c929fc6405aa795f9ae0ac5d99f |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-11T16:43:33Z |
| publishDate | 2003-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-56f38c929fc6405aa795f9ae0ac5d99f2022-12-22T00:58:15ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912003-05-0120035315Blow up of solutions to semilinear wave equationsMohammed GueddaThis 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.http://ejde.math.txstate.edu/Volumes/2003/53/abstr.htmlBlow upconformal compactification. |
| spellingShingle | Mohammed Guedda Blow up of solutions to semilinear wave equations Electronic Journal of Differential Equations Blow up conformal compactification. |
| title | Blow up of solutions to semilinear wave equations |
| title_full | Blow up of solutions to semilinear wave equations |
| title_fullStr | Blow up of solutions to semilinear wave equations |
| title_full_unstemmed | Blow up of solutions to semilinear wave equations |
| title_short | Blow up of solutions to semilinear wave equations |
| title_sort | blow up of solutions to semilinear wave equations |
| topic | Blow up conformal compactification. |
| url | http://ejde.math.txstate.edu/Volumes/2003/53/abstr.html |
| work_keys_str_mv | AT mohammedguedda blowupofsolutionstosemilinearwaveequations |