CONVERGENCE OF THE SOLUTIONS ON THE GENERALIZED KORTEWEG–DE VRIES EQUATION∗

DOI10.3846/13926292.2016.1150358zbMath1488.35477OpenAlexW2311921677MaRDI QIDQ5011617

Giuseppe Maria Coclite, Lorenzo di Ruvo

Publication date: 27 August 2021

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

Full work available at URL: https://doi.org/10.3846/13926292.2016.1150358

zbMATH Keywords

Korteweg-de Vries equationsingular limitcompensated compactnessconnected compactness

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Singular perturbations in context of PDEs (35B25) Hyperbolic conservation laws (35L65) A priori estimates in context of PDEs (35B45) Weak solutions to PDEs (35D30)

Related Items (9)

Well-posedness and blow-up for a non-local elliptic-hyperbolic system related to short-pulse equation ⋮ On the initial-boundary value problem for a Kuramoto-Sinelshchikov type equation ⋮ On a limit of perturbed conservation laws with saturating diffusion and non-positive dispersion ⋮ \(H^1\) solutions for a Kuramoto-Sinelshchikov-Cahn-Hilliard type equation ⋮ Existence results for a class of coupled Hilfer fractional pantograph differential equations with nonlocal integral boundary value conditions ⋮ A note on the convergence of the solution of the high order Camassa-Holm equation to the entropy ones of a scalar conservation law ⋮ Well-posedness of the classical solutions for a Kawahara-Korteweg-de Vries-type equation ⋮ A non-local elliptic-hyperbolic system related to the short pulse equation ⋮ On the initial-boundary value problem for a non-local elliptic-hyperbolic system related to the short pulse equation

Cites Work

• A note on the convergence of the solutions of the Camassa-Holm equation to the entropy ones of a scalar conservation law
• A singular limit problem for conservation laws related to the Kawahara-Korteweg-de Vries equation
• A singular limit problem for conservation laws related to the Kawahara equation
• Convergence of the Kuramoto-Sinelshchikov equation to the Burgers one
• Existence and regularity for solutions of the Korteweg-de Vries equation
• Large data wave operator for the generalized Korteweg-de Vries equations.
• Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension
• Remarks on the Kuramoto-Sivashinsky equation
• Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors
• 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)
• Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
• Convergence of the Ostrovsky equation to the Ostrovsky-Hunter one
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• Convergence of solution to nonlinear dispersive equations
• The zero dispersion limit for the Korteweg-deVries KdV equation
• 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.
• Minimal entropy conditions for Burgers equation
• A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation

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