Blow-up phenomena for the weakly dissipative Dullin-Gottwald-Holm equation revisited
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Publication:3192719
DOI10.1063/1.4930198zbMath1328.35188OpenAlexW1463164875MaRDI QIDQ3192719
Zai-Yun Zhang, Ming-Bao Sun, Jian Hua Huang
Publication date: 13 October 2015
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.4930198
Cauchy problemblow-upwave-breaking solutionsDullin-Gottwald-Holm equationlinear and nonlinear dispersion
PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Soliton equations (35Q51) Blow-up in context of PDEs (35B44)
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Cites Work
- Unnamed Item
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- On the behavior of the solution of the dissipative Camassa-Holm equation with the arbitrary dispersion coefficient
- Wave breaking and propagation speed for the Camassa-Holm equation with \(\kappa \neq 0\)
- Global attractor for the generalized dissipative KdV equation with nonlinearity
- On the Cauchy problem for the two-component Camassa-Holm system
- On an integrable two-component Camassa-Holm shallow water system
- Bright and dark optical solitons with time-dependent coefficients in a non-Kerr law media
- On the well-posedness of the Degasperis-Procesi equation
- Global weak solutions and blow-up structure for the Degasperis-Procesi equation
- Existence and uniqueness of low regularity solutions for the Dullin-Gottwald-Holm equation
- Global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system
- On the global existence and wave-breaking criteria for the two-component Camassa-Holm system
- Global existence and uniform decay for wave equation with dissipative term and boundary damping
- Stability analysis of heat flow with boundary time-varying delay effect
- Blow-up of solutions to the DGH equation
- Initial boundary value problems for nonlinear dispersive wave equations
- Global existence and blow-up phenomena for the weakly dissipative Camassa-Holm equation
- Blow up and propagation speed of solutions to the DGH equation
- Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time
- Wave breaking for nonlinear nonlocal shallow water equations
- Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
- On the Cauchy problem for an integrable equation with peakon solutions
- On the parametric dependences of a class of nonlinear singular maps
- Special issue on the occasion of the 50th volume
- Wave breaking for a shallow water equation
- Global weak solutions for a new periodic integrable equation with peakon solutions
- Wave-breaking and peakons for a modified Camassa-Holm equation
- Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
- A note on decay properties for the solutions of a class of partial differential equation with memory
- Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation
- On the well-posedness problem and the scattering problem for the Dullin-Gottwald-Holm equation
- Global existence and general decay for a nonlinear viscoelastic equation with nonlinear localized damping and velocity-dependent material density
- Wave-breaking phenomena, decay properties and limit behaviour of solutions of the Degasperis—Procesi equation
- Blowup and blowup rate of solutions to a weakly dissipative periodic rod equation
- On the Wave-Breaking Phenomena and Global Existence for the Generalized Periodic Camassa–Holm Equation
- Blow-up, blow-up rate and decay of the solution of the weakly dissipative Camassa-Holm equation
- Blow up, global existence, and infinite propagation speed for the weakly dissipative Camassa–Holm equation
- Blow-Up and Decay of the Solution of the Weakly Dissipative Degasperis–Procesi Equation
- Camassa–Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water waves
- An integrable shallow water equation with peaked solitons
- Global solutions to a new integrable equation with peakons
- Global existence and blow-up phenomena for a weakly dissipative 2-component Camassa–Holm system
- Global existence and uniform stabilization of a generalized dissipative Klein–Gordon equation type with boundary damping
- Blow-Up Phenomena and Decay for the Periodic Degasperis-Procesi Equation with Weak Dissipation
- On Solvability and Stabilization of a Class of Hyperbolic Hemivariational Inequalities in Elasticity
- Blow-up phenomena for the weakly dissipative Dullin–Gottwald–Holm equation