An Initial Boundary-Value Problem in a Half-Strip for the Korteweg–De Vries Equation in Fractional-Order Sobolev Spaces

DOI10.1081/PDE-200040191zbMath1080.35117MaRDI QIDQ4678902

Andrei V. Faminskii

Publication date: 23 May 2005

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

well-posednessKorteweg-de Vries equationinitial boundary-value problem

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Connections of harmonic functions with differential equations in two dimensions (31A35)

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Numerical study of the generalized Korteweg-de Vries equations with oscillating nonlinearities and boundary conditions, The Korteweg-de Vries equation on the half-line with Robin and Neumann data in low regularity spaces, KdV equation in domains with moving boundaries, Nonlocal well-posedness of the mixed problem for the Zakharov-Kuznetsov equation, A new formulation of finite difference and finite volume methods for solving a space fractional convection-diffusion model with fewer error estimates, Nonhomogeneous boundary value problems for the Korteweg-de Vries equation on a bounded domain, On the absence of global solutions of the Korteweg-de Vries equation, Asymptotic Stability of KdV Solitons on the Half-Line: A Study in the Energy Space, The Majda-Biello system on the half-line, Boundary stabilization of the Korteweg-de Vries equation and the Korteweg-de Vries-Burgers equation, Decay of solutions to damped Korteweg-de Vries type equation, Non-Homogeneous Boundary Value Problems for Linear Dispersive Equations, Control problems with an integral condition for Korteweg-de Vries equation on unbounded domains, 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, Non-homogeneous boundary value problems for the Korteweg-de Vries and the Korteweg-de Vries-Burgers equations in a quarter plane, Exponential decay of the \(H^1\)-norm for the 2D Zakharov-Kuznetsov equation on a half-strip, Well-posedness and lower bounds of the growth of weighted norms for the Schrödinger-Korteweg-de Vries interactions on the half-line, Initial boundary value problem for Korteweg-de Vries equation: a review and open problems, Initial boundary value problems for some nonlinear dispersive models on the half-line: a review and open problems, Stability of KdV solitons on the half-line, Global well-posedness and exponential decay for fifth-order Korteweg-de Vries equation posed on the finite domain, Mixed problem for the Kawahara equation in a half-strip, Non-homogeneous boundary value problems of the fifth-order KdV equations on a bounded interval, Asymptotic behavior of the Korteweg-de Vries equation posed in a quarter plane, BOUNDARY CONTROLLABILITY FOR THE TIME-FRACTIONAL NONLINEAR KORTEWEG-DE VRIES (KDV) EQUATION, Weak solutions of a mixed problem in a half-strip for a generalized Kawahara equation, The Initial-Boundary Value Problem for the Korteweg–de Vries Equation, Linear instability criterion for the Korteweg–de Vries equation on metric star graphs, A non-homogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain. II., KdV on an incoming tide

Cites Work

• Unnamed Item
• On the Korteweg-de Vries equation
• Theory of function spaces
• Existence and uniqueness of solutions for the generalized Korteweg-de Vries equation
• Remarks on the Korteweg-de Vries equation
• Solutions of the Korteweg-de Vries equation in fractional order Sobolev spaces
• Initial boundary-value problems for the Korteweg-de Vries equation
• Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
• The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices
• On the (generalized) Korteweg-de Vries equation
• Interpolation non linéaire et régularité
• A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane
• The Korteweg–de Vries Equation, Posed in a Quarter-Plane
• Uniqueness of Solutions for the Generalized Korteweg–de Vries Equation
• The initial-value problem for the Korteweg-de Vries equation
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• A Nonhomogeneous Boundary-Value Problem for the Korteweg–de Vries Equation Posed on a Finite Domain
• THE GENERALIZED KORTEWEG–DE VRIES EQUATION ON THE HALF LINE
• Sharp global well-posedness for KdV and modified KdV on ℝ and 𝕋
• A bilinear estimate with applications to the KdV equation