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arXiv · 2405.08258

On special properties of solutions to Camassa-Holm equation and related models

Christian Hong·Felipe Linares·Gustavo Ponce
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Abstract

We study unique continuation properties of solutions to the b-family of equations. This includes the Camassa-Holm and the Degasperi-Procesi models. We prove that for both, the initial value problem and the periodic boundary value problem, the unique continuation results found in \cite{LiPo} are optimal. More precisely, the result established there for the constant $c_0=0$ fails for any constant $c_0\neq 0$.

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Christian Hong, Felipe Linares, Gustavo Ponce. 2024-05-14. On special properties of solutions to Camassa-Holm equation and related models. https://arxiv.org/abs/2405.08258

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