Persistence Properties and Unique Continuation of Solutions of the Camassa-Holm Equation

By A. Alexandrou Himonas, G. Misiołek, Gustavo Ponce, Yong Zhou. 2006

252 citations recorded by the source corpus.

It is shown that a strong solution of the Camassa-Holm equation, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if it also decays exponentially at a later time. In particular, a strong solution of the Cauchy problem with compact initial profile can not be compactly supported at any later time unless it is the zero solution.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7e00bb01d6e2914bd1f859ea92b05adabaa14d95

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In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

A new asymptotic behavior of solutions to the Camassa-Holm equation (2012, methodology): “For φN (x) defined in [8], it is obvious that inequality (2.”
Blow-up of solutions to the DGH equation (2007, background): “Recently, in [22], among others, Himonas, Misiołek, Ponce and the author showed the infinite propagation speed for the Camassa–Holm equation in the sense that a strong solution of the Cauchy problem with compact initial profile cannot be compactly supported at any later time unless it is the zero so”
On a novel integrable generalization of the nonlinear Schrödinger equation (2008, background): “3) was introduced by Fuchssteiner and one of the authors in 1981 [11], it began to attract a lot of interest (see, for example [1, 4, 5, 14, 16, 18]) only after its rederivation by Camassa and Holm [3].”
On Solutions to a Two‐Component Generalized Camassa‐Holm Equation (2010, methodology): “The unique continuation and infinite propagation speed of solutions to the Camassa–Holm equation was presented by the second author and his collaborators in [21].”
Breakdown for the Camassa-Holm Equation Using Decay Criteria and Persistence in Weighted Spaces (2012, methodology): “. The exponential decay assumption for u 0 and its derivative looks optimal, as the peakons uc(x,t) = ce−|x−ct| are well-known global solutions to (1.1). This second result improves the conclusion of [20], where the authors showed that compactly supported data lead to a breakdown. 2. Analysis of the”