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Well-posedness and continuity properties of the Fornberg–Whitham equation in Besov spaces.
- Source :
-
Journal of Differential Equations . Oct2017, Vol. 263 Issue 7, p4355-4381. 27p. - Publication Year :
- 2017
-
Abstract
- In this paper, we prove well-posedness of the Fornberg–Whitham equation in Besov spaces B 2 , r s in both the periodic and non-periodic cases. This will imply the existence and uniqueness of solutions in the aforementioned spaces along with the continuity of the data-to-solution map provided that the initial data belongs to B 2 , r s . We also establish sharpness of continuity on the data-to-solution map by showing that it is not uniformly continuous from any bounded subset of B 2 , r s to C ( [ − T , T ] ; B 2 , r s ) . Furthermore, we prove a Cauchy–Kowalevski type theorem for this equation that establishes the existence and uniqueness of real analytic solutions and also provide blow-up criterion for solutions. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 263
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 124075542
- Full Text :
- https://doi.org/10.1016/j.jde.2017.05.019