Global classical solutions to the Cauchy problem for a nonlinear wave equation
In this paper we consider the Cauchy problem {u″+M(|A12u|2)Au=0 in ]0,T[u(0)=u0, u′(0)=u1, where u′ is the derivative in the sense of distributions and |A12u| is the H-norm of A12u. We prove the existence and uniqueness of global classical solution.
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| Language: | English |
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Hindawi Limited
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117129800074X |
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doaj-ca3aa7b6ee5e4d6995d5cdb27bb1f3962020-11-24T22:04:05ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121353354810.1155/S016117129800074XGlobal classical solutions to the Cauchy problem for a nonlinear wave equationHaroldo R. Clark0Universidade Federal Fluminense, Instituto de Matemática - GAN, Rua S. Paulo, 30, Niterói 24.040-110, RJ, BrazilIn this paper we consider the Cauchy problem {u″+M(|A12u|2)Au=0 in ]0,T[u(0)=u0, u′(0)=u1, where u′ is the derivative in the sense of distributions and |A12u| is the H-norm of A12u. We prove the existence and uniqueness of global classical solution.http://dx.doi.org/10.1155/S016117129800074XNonlinearwave equationglobal classical solution. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Haroldo R. Clark |
| spellingShingle |
Haroldo R. Clark Global classical solutions to the Cauchy problem for a nonlinear wave equation International Journal of Mathematics and Mathematical Sciences Nonlinear wave equation global classical solution. |
| author_facet |
Haroldo R. Clark |
| author_sort |
Haroldo R. Clark |
| title |
Global classical solutions to the Cauchy problem for a nonlinear wave equation |
| title_short |
Global classical solutions to the Cauchy problem for a nonlinear wave equation |
| title_full |
Global classical solutions to the Cauchy problem for a nonlinear wave equation |
| title_fullStr |
Global classical solutions to the Cauchy problem for a nonlinear wave equation |
| title_full_unstemmed |
Global classical solutions to the Cauchy problem for a nonlinear wave equation |
| title_sort |
global classical solutions to the cauchy problem for a nonlinear wave equation |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1998-01-01 |
| description |
In this paper we consider the Cauchy problem
{u″+M(|A12u|2)Au=0 in ]0,T[u(0)=u0, u′(0)=u1, where u′
is the derivative in the sense of distributions and |A12u| is the H-norm of
A12u. We
prove the existence and uniqueness of global classical solution. |
| topic |
Nonlinear wave equation global classical solution. |
| url |
http://dx.doi.org/10.1155/S016117129800074X |
| work_keys_str_mv |
AT haroldorclark globalclassicalsolutionstothecauchyproblemforanonlinearwaveequation |
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1725830555023441920 |