Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 92 |
| Fachzeitschrift | Nonlinear Differential Equations and Applications |
| Jahrgang | 32 |
| Ausgabenummer | 5 |
| Publikationsstatus | Veröffentlicht - 4 Juli 2025 |
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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
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in: Nonlinear Differential Equations and Applications, Jahrgang 32, Nr. 5, 92, 04.07.2025.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
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
UR - http://www.scopus.com/inward/record.url?scp=105009964449&partnerID=8YFLogxK
U2 - 10.1007/s00030-025-01096-w
DO - 10.1007/s00030-025-01096-w
M3 - Article
AN - SCOPUS:105009964449
VL - 32
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
SN - 1021-9722
IS - 5
M1 - 92
ER -