Global existence and wave breaking of solutions to the dissipative Degasperis-Procesi equation with linear dispersion

Joachim Escher; Baihong Li; Yuanhong Wei

doi:10.1007/s00030-025-01096-w

Global existence and wave breaking of solutions to the dissipative Degasperis-Procesi equation with linear dispersion

Joachim Escher^*, Baihong Li, Yuanhong Wei

^*Corresponding author for this work

Institute of Applied Mathematics

Jilin University

Research output: Contribution to journal › Article › Research › peer review

Abstract

This paper investigates the Cauchy problem associated with the Degasperis-Procesi equation modified by weak dissipation and linear dispersion. Besides well-posedness of the Cauchy problem, our focus is on exploring two critical aspects: describing conditions which imply global existence versus wave breaking phenomena of solutions. We provide sufficient conditions that guarantee global existence of solutions when both dissipation and dispersion effects are present. We also highlight the impact of the dissipativity and dispersion parameter on the qualitative behaviour of solutions such as wave breaking, presenting new insights into the dynamics of the modified Degasperis-Procesi equation.

Original language	English
Article number	92
Journal	Nonlinear Differential Equations and Applications
Volume	32
Issue number	5
DOIs	https://doi.org/10.1007/s00030-025-01096-w
Publication status	Published - 4 Jul 2025

Keywords

blow-up
Degasperis-Procesi equation
global existence
local well-posedness

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00030-025-01096-wLicence: CC BY 4.0

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title = "Global existence and wave breaking of solutions to the dissipative Degasperis-Procesi equation with linear dispersion",

abstract = "This paper investigates the Cauchy problem associated with the Degasperis-Procesi equation modified by weak dissipation and linear dispersion. Besides well-posedness of the Cauchy problem, our focus is on exploring two critical aspects: describing conditions which imply global existence versus wave breaking phenomena of solutions. We provide sufficient conditions that guarantee global existence of solutions when both dissipation and dispersion effects are present. We also highlight the impact of the dissipativity and dispersion parameter on the qualitative behaviour of solutions such as wave breaking, presenting new insights into the dynamics of the modified Degasperis-Procesi equation.",

keywords = "blow-up, Degasperis-Procesi equation, global existence, local well-posedness",

author = "Joachim Escher and Baihong Li and Yuanhong Wei",

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T1 - Global existence and wave breaking of solutions to the dissipative Degasperis-Procesi equation with linear dispersion

AU - Escher, Joachim

AU - Li, Baihong

AU - Wei, Yuanhong

N1 - Publisher Copyright: © The Author(s) 2025.

PY - 2025/7/4

Y1 - 2025/7/4

N2 - This paper investigates the Cauchy problem associated with the Degasperis-Procesi equation modified by weak dissipation and linear dispersion. Besides well-posedness of the Cauchy problem, our focus is on exploring two critical aspects: describing conditions which imply global existence versus wave breaking phenomena of solutions. We provide sufficient conditions that guarantee global existence of solutions when both dissipation and dispersion effects are present. We also highlight the impact of the dissipativity and dispersion parameter on the qualitative behaviour of solutions such as wave breaking, presenting new insights into the dynamics of the modified Degasperis-Procesi equation.

AB - This paper investigates the Cauchy problem associated with the Degasperis-Procesi equation modified by weak dissipation and linear dispersion. Besides well-posedness of the Cauchy problem, our focus is on exploring two critical aspects: describing conditions which imply global existence versus wave breaking phenomena of solutions. We provide sufficient conditions that guarantee global existence of solutions when both dissipation and dispersion effects are present. We also highlight the impact of the dissipativity and dispersion parameter on the qualitative behaviour of solutions such as wave breaking, presenting new insights into the dynamics of the modified Degasperis-Procesi equation.

KW - blow-up

KW - Degasperis-Procesi equation

KW - global existence

KW - local well-posedness

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U2 - 10.1007/s00030-025-01096-w

DO - 10.1007/s00030-025-01096-w

M3 - Article

AN - SCOPUS:105009964449

SN - 1021-9722

VL - 32

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

IS - 5

M1 - 92

ER -

Global existence and wave breaking of solutions to the dissipative Degasperis-Procesi equation with linear dispersion

Abstract

Keywords

ASJC Scopus subject areas

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