The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation
A nonlinear generalization of the Camassa-Holm equation is investigated. By making use of the pseudoparabolic regularization technique, its local well posedness in Sobolev space HS(R) with s>3/2 is established via a limiting procedure. Provided that the initial value u0 satisfies the sign conditi...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/532369 |
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| _version_ | 1832561040799301632 |
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| author | Nan Li Shaoyong Lai Shuang Li Meng Wu |
| author_facet | Nan Li Shaoyong Lai Shuang Li Meng Wu |
| author_sort | Nan Li |
| collection | DOAJ |
| description | A nonlinear generalization of the Camassa-Holm equation is investigated. By making use of the pseudoparabolic regularization technique, its local well posedness in Sobolev space HS(R) with s>3/2 is established via a limiting procedure. Provided that the initial value
u0 satisfies the sign condition and u0∈Hs(R) (s>3/2), it is shown that there exists a unique
global solution for the equation in space C([0,∞);Hs(R))∩C1([0,∞);Hs−1(R)). |
| format | Article |
| id | doaj-art-c6011f8a17e84eb8b97c46d638982eb7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c6011f8a17e84eb8b97c46d638982eb72025-02-03T01:26:08ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/532369532369The Local and Global Existence of Solutions for a Generalized Camassa-Holm EquationNan Li0Shaoyong Lai1Shuang Li2Meng Wu3Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, ChinaDepartment of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, ChinaDepartment of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, ChinaDepartment of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, ChinaA nonlinear generalization of the Camassa-Holm equation is investigated. By making use of the pseudoparabolic regularization technique, its local well posedness in Sobolev space HS(R) with s>3/2 is established via a limiting procedure. Provided that the initial value u0 satisfies the sign condition and u0∈Hs(R) (s>3/2), it is shown that there exists a unique global solution for the equation in space C([0,∞);Hs(R))∩C1([0,∞);Hs−1(R)).http://dx.doi.org/10.1155/2012/532369 |
| spellingShingle | Nan Li Shaoyong Lai Shuang Li Meng Wu The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation Abstract and Applied Analysis |
| title | The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation |
| title_full | The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation |
| title_fullStr | The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation |
| title_full_unstemmed | The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation |
| title_short | The Local and Global Existence of Solutions for a Generalized Camassa-Holm Equation |
| title_sort | local and global existence of solutions for a generalized camassa holm equation |
| url | http://dx.doi.org/10.1155/2012/532369 |
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