Global existence and blow-up phenomena for the weakly dissipative Camassa–Holm equation

2009/01/19 by Shuyin Wu, Zhaoyang Yin · 96 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Camassa–Holm equation #Dissipative system #Integrable system #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Thermodynamics

paper · pdf · doi:10.1016/j.jde.2008.12.008

published in Journal of Differential Equations 246(11), 4309-4321 (Elsevier BV)

openalex publication_date 2009/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Citations

• Global Conservative Solutions of the Camassa–Holm Equation
• Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation
• Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
• Wave breaking for nonlinear nonlocal shallow water equations

Cited by

• On the weakly dissipative Camassa–Holm, Degasperis–Procesi, and Novikov equations
• Damping-Diffusion-Noise Interactions in the Stochastic Camassa-Holm Equation
• On the weakly dissipative Camassa-Holm, Degasperis-Procesi, and Novikov equations
• New results on the global solvability and blow-up for a class of weakly dissipative Camassa-Holm equations
• Global-in-time solvability and blow-up for a non-isospectral two-component cubic Camassa-Holm system in a critical Besov space
• Existence and uniqueness of global weak solutions to a generalized Camassa-Holm equation
• Global weak solutions to a weakly dissipative μHS equation
• On the Cauchy problem of a weakly dissipative μHS equation