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Well-posedness, blow-up phenomena, and global solutions for the b-equation
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Joachim Escher
Published/Copyright:
October 29, 2008
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.
Received: 2007-03-14
Revised: 2007-07-13
Published Online: 2008-10-29
Published in Print: 2008-November
© Walter de Gruyter Berlin · New York 2008
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Articles in the same Issue
- Topology of negatively curved real affine algebraic surfaces
- The spinorial τ-invariant and 0-dimensional surgery
- Well-posedness, blow-up phenomena, and global solutions for the b-equation
- Siegel disks and periodic rays of entire functions
- Isomorphisms between Leavitt algebras and their matrix rings
- The number of smallest parts in the partitions of n
- Modular analogues of Jordan's theorem for finite linear groups
- Prime specialization in higher genus I
- Filling inequalities do not depend on topology
- Erratum to "Modular curves and Ramanujan's continued fraction"
