Global Weak Solution for a generalized Camassa-Holm equation
Xi Tu, Zhaoyang Yin
TL;DR
This paper investigates the Cauchy problem for a generalized Camassa-Holm equation, establishing conditions for global existence, blow-up, and proving the existence and uniqueness of global weak solutions.
Contribution
It introduces new global existence and blow-up results for the generalized Camassa-Holm equation and proves the existence and uniqueness of its global weak solutions.
Findings
Two global existence results
Two blow-up results
Existence and uniqueness of global weak solutions
Abstract
In this paper we mainly investigate the Cauchy problem of a generalized Camassa-Holm equation. First by this relationship between the Degasperis-Procesi equation and the generalized Camassa-Holm equation, we then obtain two global existences result and two blow-up result. Then, we prove the existence and uniqueness of global weak solutions.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Differential Equations and Dynamical Systems · Algebraic structures and combinatorial models