Uniform stabilization of numerical schemes for the critical generalized Korteweg-de Vries equation with damping

DOI10.1007/s00211-010-0291-xzbMath1198.65181OpenAlexW2042518967MaRDI QIDQ993372

Mauricio Sepúlveda, Octavio P. Vera Villagrán, Ademir Fernando Pazoto

Publication date: 10 September 2010

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10533/144524

zbMATH Keywords

stabilitynumerical experimentsfinite differenceKorteweg-de Vries equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (14)

Convergence of a finite difference method for the KdV and modified KdV equations with \(L^2\) data ⋮ On the asymptotic stability of the Korteweg-de Vries equation with time-delayed internal feedback ⋮ Global Stabilization of a Korteweg--De Vries Equation With Saturating Distributed Control ⋮ Delayed stabilization of the Korteweg-de Vries equation on a star-shaped network ⋮ A finite difference scheme for smooth solutions of the general Degasperis–Procesi equation ⋮ Interaction of solitary waves for the generalized KdV equation ⋮ Pseudo-Backstepping and Its Application to the Control of Korteweg--de Vries Equation from the Right Endpoint on a Finite Domain ⋮ Cone-bounded feedback laws for \(m\)-dissipative operators on Hilbert spaces ⋮ Output feedback stabilization of the Korteweg-de Vries equation ⋮ Stability properties of a higher order scheme for a GKdV-4 equation modelling surface water waves ⋮ Finite difference scheme for a higher order nonlinear Schrödinger equation ⋮ Output feedback stabilization of the linearized Korteweg-de Vries equation with right endpoint controllers ⋮ Well-posedness and asymptotic behavior of a generalized higher order nonlinear Schrödinger equation with localized dissipation ⋮ Interaction of solitons and the effect of radiation for the generalized KdV equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical solution of KdV-KdV systems of Boussinesq equations. I: The numerical scheme and generalized solitary waves
• Best constants for Gagliardo-Nirenberg inequalities on the real line
• Coupled system of Korteweg-de Vries equations type in domains with moving boundaries
• On the inverse of a general pentadiagonal matrix
• Compact sets in the space \(L^ p(0,T;B)\)
• An introduction to partial differential equations
• Uniform exponential long time decay for the space semi-discretization of a locally damped wave equation via an artificial numerical viscosity
• Multisymplectic box schemes and the Korteweg-de Vries equation.
• Spatially accurate dissipative or conservative finite difference schemes derived by the discrete variational method
• Finite difference schemes for \(\frac{\partial u}{\partial t}=(\frac{\partial}{\partial x})^\alpha\frac{\delta G}{\delta u}\) that inherit energy conservation or dissipation property
• The Korteweg-de Vries-Kawahara equation in a bounded domain and some numerical results
• Existence of blow-up solutions in the energy space for the critical generalized KdV equation
• Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
• Unique continuation and decay for the Korteweg-de Vries equation with localized damping
• On the exponential decay of the critical generalized Korteweg-de Vries equation with localized damping
• Global Stabilization of the Generalized Korteweg--de Vries Equation Posed on a Finite Domain
• Uniform stabilization of a viscous numerical approximation for a locally damped wave equation
• Convergence of Galerkin Approximations for the Korteweg-de Vries Equation
• Stability and instability of solitary waves of Korteweg-de Vries type
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Stabilization of the Korteweg-de Vries equation with localized damping
• Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation
• On the uniform decay for the Korteweg–de Vries equation with weak damping
• Why are solitons stable?
• A semi-implicit monotone difference scheme for an initial-boundary value problem of a strongly degenerate parabolic equation modeling sedimentation-consolidation processes
• Implicit Runge-Kutta Processes
• Instability of solitons for the critical generalized Korteweg-de Vries equation
• An initial-boundary-value problem that approximates the quarter-plane problem for the Korteweg-de Vries equation

This page was built for publication: Uniform stabilization of numerical schemes for the critical generalized Korteweg-de Vries equation with damping