Odd-order quasilinear evolution equations posed on a bounded interval
We study in a rectangle Q_T = (0, T)×(0, 1) global well-posedness of nonhomo-geneous initial-boundary value problems for general odd-order quasilinear partial differential equations. This class of equations includes well-known Korteweg–de Vries and Kawahara equations which model the dynamics of long...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2010-07-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/10816/5838 |
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| author | Andrei V. Faminskii Nikolai A. Larkin |
| author_facet | Andrei V. Faminskii Nikolai A. Larkin |
| author_sort | Andrei V. Faminskii |
| collection | DOAJ |
| description | We study in a rectangle Q_T = (0, T)×(0, 1) global well-posedness of nonhomo-geneous initial-boundary value problems for general odd-order quasilinear partial differential equations. This class of equations includes well-known Korteweg–de Vries and Kawahara equations which model the dynamics of long small-amplitude waves in various media. Our study is motivated by physics and numerics and our main goal is to formulate a correct nonhomogeneous initial-boundary value problem under consideration in a bounded interval and to prove the existence and uniqueness of global in time weak and regular solutions in a large scale of Sobolev spaces as well as to study decay of solutions while t → ∞. |
| first_indexed | 2024-04-12T09:56:50Z |
| format | Article |
| id | doaj.art-da97932e8da14baab788ece2b901a469 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-04-12T09:56:50Z |
| publishDate | 2010-07-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-da97932e8da14baab788ece2b901a4692022-12-22T03:37:41ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882010-07-012816777Odd-order quasilinear evolution equations posed on a bounded intervalAndrei V. FaminskiiNikolai A. LarkinWe study in a rectangle Q_T = (0, T)×(0, 1) global well-posedness of nonhomo-geneous initial-boundary value problems for general odd-order quasilinear partial differential equations. This class of equations includes well-known Korteweg–de Vries and Kawahara equations which model the dynamics of long small-amplitude waves in various media. Our study is motivated by physics and numerics and our main goal is to formulate a correct nonhomogeneous initial-boundary value problem under consideration in a bounded interval and to prove the existence and uniqueness of global in time weak and regular solutions in a large scale of Sobolev spaces as well as to study decay of solutions while t → ∞.http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/10816/5838Korteweg–de VriesKawahara. |
| spellingShingle | Andrei V. Faminskii Nikolai A. Larkin Odd-order quasilinear evolution equations posed on a bounded interval Boletim da Sociedade Paranaense de Matemática Korteweg–de Vries Kawahara. |
| title | Odd-order quasilinear evolution equations posed on a bounded interval |
| title_full | Odd-order quasilinear evolution equations posed on a bounded interval |
| title_fullStr | Odd-order quasilinear evolution equations posed on a bounded interval |
| title_full_unstemmed | Odd-order quasilinear evolution equations posed on a bounded interval |
| title_short | Odd-order quasilinear evolution equations posed on a bounded interval |
| title_sort | odd order quasilinear evolution equations posed on a bounded interval |
| topic | Korteweg–de Vries Kawahara. |
| url | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/10816/5838 |
| work_keys_str_mv | AT andreivfaminskii oddorderquasilinearevolutionequationsposedonaboundedinterval AT nikolaialarkin oddorderquasilinearevolutionequationsposedonaboundedinterval |