An initial-boundary-value problem that approximates the quarter-plane problem for the Korteweg-de Vries equation

DOI10.1016/S0362-546X(00)00155-3zbMath1027.35111WikidataQ127360312 ScholiaQ127360312MaRDI QIDQ5953910

Marguerite Gisclon, Thierry Colin

Publication date: 22 April 2002

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

zbMATH Keywords

existenceKorteweg-de Vries equationfinite-difference schemequarter-planesmoothing effects

Mathematics Subject Classification ID

Related Items (17)

The Korteweg-de Vries-Kawahara equation in a bounded domain and some numerical results ⋮ Global regular solutions for the 3D Zakharov-Kuznetsov equation posed on unbounded domains ⋮ On the asymptotic stability of the Korteweg-de Vries equation with time-delayed internal feedback ⋮ Delayed stabilization of the Korteweg-de Vries equation on a star-shaped network ⋮ Stability results for the KdV equation with time-varying delay ⋮ The existence of strong solutions to the 3D Zakharov-Kuznestov equation in a bounded domain ⋮ Well-posedness for the \(BBM\)-equation in a quarter plane ⋮ Coupled system of Korteweg-de Vries equations type in domains with moving boundaries ⋮ The Kawahara equation on bounded intervals and on a half-line ⋮ Local existence of strong solutions to the 3D Zakharov-Kuznetsov equation in a bounded domain ⋮ Global regular solutions to one problem of Saut-Temam for the 3D Zakharov-Kuznetsov equation ⋮ Controllability problems for the Korteweg-de Vries equation with integral overdetermination ⋮ Stability of some stationary solutions to the forced KdV equation with one or two bumps ⋮ Neumann problem for the Korteweg--de Vries equation ⋮ Uniform stabilization of numerical schemes for the critical generalized Korteweg-de Vries equation with damping ⋮ Asymptotic behavior of the Korteweg-de Vries equation posed in a quarter plane ⋮ An initial and boundary-value problem for the Zakharov-Kuznestov equation in a bounded domain

Cites Work

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• The Korteweg-de Vries equation in a quarter plane, continuous dependence results
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• Sur un problème non linéaire
• The Korteweg–de Vries Equation, Posed in a Quarter-Plane
• The initial-value problem for the Korteweg-de Vries equation
• Un problème mixte pour l’équation de Korteweg-de Vries sur un intervalle borné
• Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation
• A bilinear estimate with applications to the KdV equation

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