Well-posedness and blow-up phenomena for the generalized Degasperis-Procesi equation

DOI10.1016/J.NA.2010.03.006zbMath1194.35080OpenAlexW1976146710MaRDI QIDQ975248

Zhaoyang Yin, Xinglong Wu

Publication date: 9 June 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.03.006

zbMATH Keywords

Cauchy problemwell-posednesslocal well-posednessequilibrium pointblow-up phenomenablow-up scenariogeneralized Degasperis-Procesi equation

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Blow-up in context of PDEs (35B44) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (3)

Blow-up phenomena and stability of solitary waves for a generalized Dullin-Gottwald-Holm equation ⋮ Non-uniform dependence on initial data for the generalized Degasperis–Procesi equation on the line ⋮ The Cauchy problem for a dissipative periodic 2-component Degasperis-Procesi system

Cites Work

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• On the Korteweg-de Vries equation
• On the well-posedness of the Degasperis-Procesi equation
• Global weak solutions and blow-up structure for the Degasperis-Procesi equation
• Stability of a class of solitary waves in compressible elastic rods
• Semigroups of linear operators and applications to partial differential equations
• Acoustic scattering and the extended Korteweg-de Vries hierarchy
• Wave breaking for nonlinear nonlocal shallow water equations
• On the Cauchy problem for the periodic Camassa-Holm equation
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Global existence for a new periodic integrable equation.
• On the Cauchy problem for an integrable equation with peakon solutions
• Geodesic flow on the diffeomorphism group of the circle
• Traveling wave solutions of the Degasperis-Procesi equation
• The initial value problem for a generalized Boussinesq equation.
• Periodic and solitary-wave solutions of the Degasperis-Procesi equation
• Global weak solutions for a new periodic integrable equation with peakon solutions
• On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• Global existence and blow-up phenomena for the Degasperis-Procesi equation
• Infinite propagation speed for the Degasperis-Procesi equation
• On the scattering problem for the Camassa-Holm equation
• Finite propagation speed for the Camassa–Holm equation
• Commutator estimates and the euler and navier-stokes equations
• The initial-value problem for the Korteweg-de Vries equation
• Multi-peakons and a theorem of Stieltjes
• A shallow water equation on the circle
• Wave Structure and Nonlinear Balances in a Family of Evolutionary PDEs
• Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves
• Multi-peakon solutions of the Degasperis–Procesi equation
• Stability of peakons
• An integrable shallow water equation with peaked solitons
• A Note on the Degasperis-Procesi Equation
• Global solutions to a new integrable equation with peakons
• Multisoliton solutions of the Degasperis–Procesi equation and their peakon limit
• On the Cauchy problem for the generalized Camassa-Holm equation
• On the Cauchy problem for a generalized Camassa-Holm equation

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