Dispersive estimates for a linear wave equation with electromagnetic potential
We consider radial solutions to the Cauchy problem for a linear wave equation with a small short-range electromagnetic potential (depending on space and time) and zero initial data. We present two dispersive estimates that provide, in particular, an optimal decay rate in time $t^{-1}$ for the so...
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| Language: | English |
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Texas State University
2008-10-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2008/150/abstr.html |
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doaj-35b43e25b0b04f6996a5d0fd28f9b5212020-11-24T21:48:57ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912008-10-012008150,112Dispersive estimates for a linear wave equation with electromagnetic potentialDavide CataniaWe consider radial solutions to the Cauchy problem for a linear wave equation with a small short-range electromagnetic potential (depending on space and time) and zero initial data. We present two dispersive estimates that provide, in particular, an optimal decay rate in time $t^{-1}$ for the solution. Also, we apply these estimates to obtain similar results for the linear massless Dirac equation perturbed by a potential.http://ejde.math.txstate.edu/Volumes/2008/150/abstr.htmlWave equationelectromagnetic potentialshort-rangeDirac equationdispersive estimatedecay estimate |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Davide Catania |
| spellingShingle |
Davide Catania Dispersive estimates for a linear wave equation with electromagnetic potential Electronic Journal of Differential Equations Wave equation electromagnetic potential short-range Dirac equation dispersive estimate decay estimate |
| author_facet |
Davide Catania |
| author_sort |
Davide Catania |
| title |
Dispersive estimates for a linear wave equation with electromagnetic potential |
| title_short |
Dispersive estimates for a linear wave equation with electromagnetic potential |
| title_full |
Dispersive estimates for a linear wave equation with electromagnetic potential |
| title_fullStr |
Dispersive estimates for a linear wave equation with electromagnetic potential |
| title_full_unstemmed |
Dispersive estimates for a linear wave equation with electromagnetic potential |
| title_sort |
dispersive estimates for a linear wave equation with electromagnetic potential |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2008-10-01 |
| description |
We consider radial solutions to the Cauchy problem for a linear wave equation with a small short-range electromagnetic potential (depending on space and time) and zero initial data. We present two dispersive estimates that provide, in particular, an optimal decay rate in time $t^{-1}$ for the solution. Also, we apply these estimates to obtain similar results for the linear massless Dirac equation perturbed by a potential. |
| topic |
Wave equation electromagnetic potential short-range Dirac equation dispersive estimate decay estimate |
| url |
http://ejde.math.txstate.edu/Volumes/2008/150/abstr.html |
| work_keys_str_mv |
AT davidecatania dispersiveestimatesforalinearwaveequationwithelectromagneticpotential |
| _version_ |
1725890384858447872 |