A note on the convergence of the solutions of the Camassa-Holm equation to the entropy ones of a scalar conservation law
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Publication:255894
DOI10.3934/dcds.2016.36.2981zbMath1336.35056OpenAlexW4248573216MaRDI QIDQ255894
Giuseppe Maria Coclite, Lorenzo di Ruvo
Publication date: 9 March 2016
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcds.2016.36.2981
shallow water equationsingular limitcompensated compactnessentropy conditionnonlinear dispersive effects
Asymptotic behavior of solutions to PDEs (35B40) Hyperbolic conservation laws (35L65) Initial value problems for nonlinear higher-order PDEs (35G25)
Related Items (13)
On the convergence of the modified Rosenau and the modified Benjamin-Bona-Mahony equations ⋮ A note on convergence of the solutions of Benjamin-Bona-Mahony type equations ⋮ On \(H^2\)-solutions for a Camassa-Holm type equation ⋮ Energy conservation and well-posedness of the Camassa-Holm equation in Sobolev spaces ⋮ On the classical solutions for the high order Camassa-Holm type equations ⋮ On a Hamiltonian regularization of scalar conservation laws ⋮ Infinite propagation speed and asymptotic behavior for a generalized fifth-order Camassa–Holm equation ⋮ An asymptotic property of the Camassa-Holm equation on the half-line ⋮ Convergence of the Kuramoto-Sinelshchikov equation to the Burgers one ⋮ A note on the convergence of the solution of the high order Camassa-Holm equation to the entropy ones of a scalar conservation law ⋮ Transfer of energy in Camassa-Holm and related models by use of nonunique characteristics ⋮ Singular limits with vanishing viscosity for nonlocal conservation laws ⋮ CONVERGENCE OF THE SOLUTIONS ON THE GENERALIZED KORTEWEG–DE VRIES EQUATION∗
Cites Work
- Unnamed Item
- A singular limit problem for conservation laws related to the Rosenau-Korteweg-de Vries equation
- Analyticity of periodic traveling free surface water waves with vorticity
- Dissipative solutions for the Camassa-Holm equation
- The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
- The trajectories of particles in Stokes waves
- Global conservative solutions of the Camassa-Holm equation
- Global conservative solutions of the generalized hyperelastic-rod wave equation
- Singular limit problem of the Camassa-Holm type equation
- An explicit finite difference scheme for the Camassa-Holm equation
- The embedding of the positive cone of $H^{-1}$ in $W^{-1,\,q}$ is compact for all $q<2$ (with a remark of Haim Brezis)
- Wave breaking for nonlinear nonlocal shallow water equations
- Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
- Special issue on the occasion of the 50th volume
- Global weak solutions for a shallow water equation
- The Cauchy problem for an integrable shallow-water equation
- Analytic solutions and singularity formation for the peakon \(b\)-family equations
- Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
- A note on the Camassa-Holm equation
- Well-posedness of higher-order Camassa-Holm equations
- Wellposedness for a parabolic-elliptic system
- On the weak solutions to a shallow water equation
- KINETIC DECOMPOSITION OF APPROXIMATE SOLUTIONS TO CONSERVATION LAWS: APPLICATION TO RELAXATION AND DIFFUSION-DISPERSION APPROXIMATIONS*
- Particle trajectories in extreme Stokes waves
- GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
- Variational derivation of the Camassa-Holm shallow water equation
- A Convergent Finite Difference Scheme for the Camassa–Holm Equation with General $H^1$ Initial Data
- Convergence of solution to nonlinear dispersive equations
- Conservation laws with vanishing nonlinear diffusion and dispersion11This work was partially carried out during a visit of the first author to the Istituto per le Applicazioni del Calcolo.
- Global weak solutions for a shallow water equation
- An integrable shallow water equation with peaked solitons
- Camassa–Holm, Korteweg–de Vries and related models for water waves
- Minimal entropy conditions for Burgers equation
- ON THE UNIQUENESS AND LARGE TIME BEHAVIOR OF THE WEAK SOLUTIONS TO A SHALLOW WATER EQUATION
- Solitary shock waves and other travelling waves in a general compressible hyperelastic rod
- Particle trajectories in solitary water waves
- Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View
- Global Weak Solutions to a Generalized Hyperelastic-rod Wave Equation
- A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation
- On the Cauchy problem for the Camassa-Holm equation
- Exact travelling-wave solutions of an integrable equation arising in hyperelastic rods.
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