The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces
This paper is concerned with the periodic boundary value problem for a quasilinear evolution equation of the following type: ∂tu+f(u)∂xu+F(u)=0, x∈T=R/2πZ, t∈R+. Under some conditions, we prove that this equation is locally well-posed in Besov space Bp,rs(T). Furthermore, we study the continuity of...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/862593 |
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| _version_ | 1832556057145114624 |
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| author | Yun Wu Zhengrong Liu Xiang Zhang |
| author_facet | Yun Wu Zhengrong Liu Xiang Zhang |
| author_sort | Yun Wu |
| collection | DOAJ |
| description | This paper is concerned with the periodic boundary value problem for a quasilinear evolution equation of the following type: ∂tu+f(u)∂xu+F(u)=0, x∈T=R/2πZ, t∈R+. Under some conditions, we prove that this equation is locally well-posed in Besov space Bp,rs(T). Furthermore, we study the continuity of the solution map for this equation in B2,rs(T). Our work improves some earlier results. |
| format | Article |
| id | doaj-art-38a109d2cc5d4fa38e5357f961ee088b |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-38a109d2cc5d4fa38e5357f961ee088b2025-02-03T05:46:28ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/862593862593The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov SpacesYun Wu0Zhengrong Liu1Xiang Zhang2Department of Mathematics and Computer Science, Guizhou Normal University, Guiyang, Guizhou 550001, ChinaSchool of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, ChinaDepartment of Mathematics and Computer Science, Guizhou Normal University, Guiyang, Guizhou 550001, ChinaThis paper is concerned with the periodic boundary value problem for a quasilinear evolution equation of the following type: ∂tu+f(u)∂xu+F(u)=0, x∈T=R/2πZ, t∈R+. Under some conditions, we prove that this equation is locally well-posed in Besov space Bp,rs(T). Furthermore, we study the continuity of the solution map for this equation in B2,rs(T). Our work improves some earlier results.http://dx.doi.org/10.1155/2015/862593 |
| spellingShingle | Yun Wu Zhengrong Liu Xiang Zhang The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces Journal of Function Spaces |
| title | The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces |
| title_full | The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces |
| title_fullStr | The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces |
| title_full_unstemmed | The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces |
| title_short | The Periodic Boundary Value Problem for a Quasilinear Evolution Equation in Besov Spaces |
| title_sort | periodic boundary value problem for a quasilinear evolution equation in besov spaces |
| url | http://dx.doi.org/10.1155/2015/862593 |
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