Conserved quantities, continuation and compactly supported solutions of some shallow water models

Abstract

A proof that strong solutions of the Dullin-Gottwald-Holm equation vanishing on an open set of the (1+1) space-time are identically zero is presented. In order to do it, we use a geometrical approach based on the conserved quantities of the equation to prove a unique continuation result for its solutions. We show that this idea can be applied to a large class of equations of the Camassa-Holm type.

arXiv commentMajor modifications in the original file. Inclusion of new results and references. Improvement of the discussion of the results

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Cited by in corpus (6)

• Existence, continuation, persistence and dynamics of solutions for a generalized 0-Holm-Staley equation
• A geometrical demonstration for continuation of solutions of the generalised BBM equation
• Geometrical demonstration for persistence properties for a bi-Hamiltonian shallow water system
• The Cauchy problem and continuation of periodic solutions for a generalized Camassa-Holm equation
• Persistence properties of a Camassa-Holm type equation with $(n+1)-$order non-linearities
• Unique continuation results for abstract quasi-linear evolution equations in Banach spaces