The critical case for a semilinear weakly hyperbolic equation
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 $t_0$ greater than zero with $a(t_0)=0$, and $p(lambd...
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| Format: | Article |
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Texas State University
2004-08-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2004/101/abstr.thml |
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doaj-749e5525115d44f9aba65dc2c497f7f02020-11-25T01:25:41ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912004-08-012004101113The critical case for a semilinear weakly hyperbolic equationLuca FanelliSandra LucenteWe 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 $t_0$ greater than zero with $a(t_0)=0$, and $p(lambda)=(3lambda+10)/(3lambda+2)$ with $3le p(lambda)le 5$. This means that we deal with the superconformal, critical nonlinear case. Moreover we assume a small initial energy. http://ejde.math.txstate.edu/Volumes/2004/101/abstr.thmlGlobal existencesemilinear wave equations. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Luca Fanelli Sandra Lucente |
| spellingShingle |
Luca Fanelli Sandra Lucente The critical case for a semilinear weakly hyperbolic equation Electronic Journal of Differential Equations Global existence semilinear wave equations. |
| author_facet |
Luca Fanelli Sandra Lucente |
| author_sort |
Luca Fanelli |
| title |
The critical case for a semilinear weakly hyperbolic equation |
| title_short |
The critical case for a semilinear weakly hyperbolic equation |
| title_full |
The critical case for a semilinear weakly hyperbolic equation |
| title_fullStr |
The critical case for a semilinear weakly hyperbolic equation |
| title_full_unstemmed |
The critical case for a semilinear weakly hyperbolic equation |
| title_sort |
critical case for a semilinear weakly hyperbolic equation |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2004-08-01 |
| description |
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 $t_0$ greater than zero with $a(t_0)=0$, and $p(lambda)=(3lambda+10)/(3lambda+2)$ with $3le p(lambda)le 5$. This means that we deal with the superconformal, critical nonlinear case. Moreover we assume a small initial energy. |
| topic |
Global existence semilinear wave equations. |
| url |
http://ejde.math.txstate.edu/Volumes/2004/101/abstr.thml |
| work_keys_str_mv |
AT lucafanelli thecriticalcaseforasemilinearweaklyhyperbolicequation AT sandralucente thecriticalcaseforasemilinearweaklyhyperbolicequation AT lucafanelli criticalcaseforasemilinearweaklyhyperbolicequation AT sandralucente criticalcaseforasemilinearweaklyhyperbolicequation |
| _version_ |
1725112496977608704 |