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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |