Global weak solutions and breaking waves to the Degasperis-Procesi equation with linear dispersion

DOI10.1016/j.jmaa.2009.08.010zbMath1180.35006OpenAlexW2025458968MaRDI QIDQ1034555

Fei Guo

Publication date: 6 November 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.08.010

zbMATH Keywords

initial value problemglobal weak solutionDegasperis-Procesi equationpeaked solitonsstrong dispersion

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence problems for PDEs: global existence, local existence, non-existence (35A01)

Related Items (2)

Limit behavior of the global solutions to the Degasperis-Procesi-type equation ⋮ Orbital stability of peakons for the Degasperis-Procesi equation with strong dispersion

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Two new types of bounded waves of CH-\(\gamma\) equation
• Global weak solutions and wave breaking phenomena to the periodic Degasperis-Procesi equation with strong dispersion
• Peaked wave solutions of CH-r equation
• On the well-posedness of the Degasperis-Procesi equation
• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Global weak solutions and blow-up structure for the Degasperis-Procesi equation
• The trajectories of particles in Stokes waves
• Formation and dynamics of shock waves in the Degasperis-Procesi equation
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Wave breaking for nonlinear nonlocal shallow water equations
• On the Cauchy problem for an integrable equation with peakon solutions
• Global weak solutions for a shallow water equation
• KdV dynamics in the plasma-sheath transition.
• Nonlinear balance and exchange of stability in dynamics of solitons, peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary PDE
• Wave breaking for a shallow water equation
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• On the initial-value problem to the Degasperis-Procesi equation with linear dispersion
• Global existence and blow-up phenomena for the Degasperis-Procesi equation
• Infinite propagation speed for the Degasperis-Procesi equation
• Existence of permanent and breaking waves for the periodic Degasperis–Procesi equation with linear dispersion
• Wave Breaking in a Class of Nonlocal Dispersive Wave Equations
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Multi-peakon solutions of the Degasperis–Procesi equation
• Stability of peakons
• An integrable shallow water equation with peaked solitons
• Camassa–Holm, Korteweg–de Vries and related models for water waves
• Global solutions to a new integrable equation with peakons
• Particle trajectories in solitary water waves
• On the Blow-up Phenomena for the Degasperis-Procesi Equation
• Multisoliton solutions of the Degasperis–Procesi equation and their peakon limit
• Local well‐posedness and blow‐up criteria of solutions for a rod equation

This page was built for publication: Global weak solutions and breaking waves to the Degasperis-Procesi equation with linear dispersion