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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 17
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Research Article

Wave-breaking phenomena and persistence properties for a nonlinear dissipative Camassa–Holm equation

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Pages 4805-4827 | Received 09 Jul 2022, Accepted 09 Oct 2022, Published online: 01 Nov 2022
 

Abstract

In present paper, we mainly consider the wave-breaking phenomena and persistence properties of a nonlinear dissipative Camassa–Holm equation. The precise blow-up criteria of the Cauchy problem are established and wave-breaking phenomenon is investigated based on the method of characteristics and the Riccati-type differential inequality. Due to the presence of high order nonlinear term, the conservation law E=Ru2+ux2dx is losed. This difficulty has been addressed by establishing the energy inequality. Finally, we establish the persistence properties and some unique continuation properties of the solutions in the weighted Lp-spaces Lϕp(R):=Lp(R,ϕpdx).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China [No. 11701068].

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