The Local Strong Solutions and Global Weak Solutions for a Nonlinear Equation
The existence and uniqueness of local strong solutions for a nonlinear equation are investigated in the Sobolev space C([0,T);Hs(R)) ∩C1([0,T);Hs-1(R)) provided that the initial value lies in Hs(R) with s>3/2. Meanwhile, we prove the existence of global weak solutions in L∞([0,∞);L2(R)) for the e...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/619068 |
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| _version_ | 1832556963203907584 |
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| author | Meng Wu |
| author_facet | Meng Wu |
| author_sort | Meng Wu |
| collection | DOAJ |
| description | The existence and uniqueness of local strong solutions for a nonlinear equation are investigated in the Sobolev space C([0,T);Hs(R)) ∩C1([0,T);Hs-1(R)) provided that the initial value lies in Hs(R) with s>3/2. Meanwhile, we prove the existence of global weak solutions in L∞([0,∞);L2(R)) for the equation. |
| format | Article |
| id | doaj-art-8f0e9e9e8b1b4af592e9c1698fe2e8b6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-8f0e9e9e8b1b4af592e9c1698fe2e8b62025-02-03T05:43:56ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/619068619068The Local Strong Solutions and Global Weak Solutions for a Nonlinear EquationMeng Wu0Department of Mathematics, Southwestern University of Finance and Economics, Chengdu 610074, ChinaThe existence and uniqueness of local strong solutions for a nonlinear equation are investigated in the Sobolev space C([0,T);Hs(R)) ∩C1([0,T);Hs-1(R)) provided that the initial value lies in Hs(R) with s>3/2. Meanwhile, we prove the existence of global weak solutions in L∞([0,∞);L2(R)) for the equation.http://dx.doi.org/10.1155/2013/619068 |
| spellingShingle | Meng Wu The Local Strong Solutions and Global Weak Solutions for a Nonlinear Equation Abstract and Applied Analysis |
| title | The Local Strong Solutions and Global Weak Solutions for a Nonlinear Equation |
| title_full | The Local Strong Solutions and Global Weak Solutions for a Nonlinear Equation |
| title_fullStr | The Local Strong Solutions and Global Weak Solutions for a Nonlinear Equation |
| title_full_unstemmed | The Local Strong Solutions and Global Weak Solutions for a Nonlinear Equation |
| title_short | The Local Strong Solutions and Global Weak Solutions for a Nonlinear Equation |
| title_sort | local strong solutions and global weak solutions for a nonlinear equation |
| url | http://dx.doi.org/10.1155/2013/619068 |
| work_keys_str_mv | AT mengwu thelocalstrongsolutionsandglobalweaksolutionsforanonlinearequation AT mengwu localstrongsolutionsandglobalweaksolutionsforanonlinearequation |