Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equations in a quarter plane

DOI10.1016/j.anihpc.2007.07.006zbMath1157.35090OpenAlexW2071654613MaRDI QIDQ957585

Bing-Yu Zhang, Jerry L. Bona, Shu Ming Sun

Publication date: 28 November 2008

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/78827

zbMATH Keywords

Korteweg-de Vries equationKorteweg-de Vries-Burgers equationinitial-boundary-value problemsnonlinear dispersive wave equations

Mathematics Subject Classification ID

Related Items (39)

The derivative nonlinear Schrödinger equation on the half line ⋮ Kawahara-Burgers equation on a strip ⋮ Higher-order stationary dispersive equations on bounded intervals ⋮ Lower regularity solutions of the non-homogeneous boundary-value problem for a higher order Boussinesq equation in a quarter plane ⋮ A higher dispersion KdV equation on the half-line ⋮ Global regular solutions for the 3D Zakharov-Kuznetsov equation posed on unbounded domains ⋮ Dispersion estimates for the boundary integral operator associated with the fourth order Schrödinger equation posed on the half line ⋮ Low regularity solutions of non-homogeneous boundary value problems of a higher order Boussinesq equation in a quarter plane ⋮ Nonhomogeneous boundary value problems for the Korteweg-de Vries equation on a bounded domain ⋮ Unnamed Item ⋮ Global controllability and stabilizability of Kawahara equation on a periodic domain ⋮ Stabilization of Regular Solutions for the Zakharov-Kuznetsov Equation Posed on Bounded Rectangles and on a Strip ⋮ Nonhomogeneous boundary-value problems for one-dimensional nonlinear Schrödinger equations ⋮ Stratonovich–Khasminskii averaging principle for multiscale random Korteweg–de Vries-Burgers equation ⋮ Boundary value problem for the KdV-Burgers equation in a quarter plane ⋮ Parameter estimation and output feedback stabilization for the linear Korteweg-de Vries equation with disturbed boundary measurement ⋮ Boundary stabilization of the Korteweg-de Vries equation and the Korteweg-de Vries-Burgers equation ⋮ Wellposedness of the sixth order Boussinesq equation with non-homogeneous boundary values on a bounded domain ⋮ Control and stabilization of the Korteweg-de Vries equation: recent progresses ⋮ Motion of a vortex filament with axial flow in the half space ⋮ The 2D Kawahara equation on a half-strip ⋮ Boundary smoothing properties of the Kawahara equation posed on the finite domain ⋮ A non-homogeneous boundary-value problem for the KdV-Burgers equation posed on a finite domain ⋮ The Korteweg-de Vries equation on a metric star graph ⋮ Global regular solutions for the 3D Kawahara equation posed on unbounded domains ⋮ Exponential decay of the \(H^1\)-norm for the 2D Zakharov-Kuznetsov equation on a half-strip ⋮ Nonlinear Fourier Transforms and the mKdV Equation in the Quarter Plane ⋮ Global well-posedness and exponential decay for fifth-order Korteweg-de Vries equation posed on the finite domain ⋮ Non-homogeneous boundary value problems of the fifth-order KdV equations on a bounded interval ⋮ BOUNDARY CONTROLLABILITY FOR THE TIME-FRACTIONAL NONLINEAR KORTEWEG-DE VRIES (KDV) EQUATION ⋮ The KdV Equation on the Half-Line: Time-Periodicity and Mass Transport ⋮ Linear instability criterion for the Korteweg–de Vries equation on metric star graphs ⋮ Well-posedness of the generalized Burgers equation on a finite interval ⋮ A non-homogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain. II. ⋮ Kato smoothing properties of a class of nonlinear dispersive wave equations on a periodic domain ⋮ Unnamed Item ⋮ Sharp Kato smoothing properties of weakly dissipated KdV equations with variable coefficients on a periodic domain ⋮ Computable analysis of a boundary-value problem for the generalized KdV-Burgers equation ⋮ Well-posedness and stability results for the Korteweg-de Vries-Burgers and Kuramoto-Sivashinsky equations with infinite memory: a history approach

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