Abstract: | |
In the paper we first establish the local well-posedness for a family of nonlinear dispersive equations, the so called b-equation. Then we describe the precise blow-up scenario. Moreover, we prove that for the b-equation we do have the coexistence of global in time solutions and blow-up phenomena: Depending on the initial data solutions may exist for ever, while other data force the solution to produce a singularity in finite time. Finally, we prove the uniqueness and existence of global weak solution to the equation provided the initial data satisfy certain sign conditions.
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License of this version: | Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich. |
Publication type: | Article |
Publishing status: | publishedVersion |
Publication date: | 2008-10-29 |
Keywords english: | degasperis-procesi equation, shallow-water equation, camassa-holm equation, korteweg-de-vries, integrable equation, peakon solutions, weak solutions, cauchy-problem, wave solutions, shock-waves |
DDC: | 510 | Mathematik |
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