The Korteweg–de Vries Equation on a Periodic Domain with Singular-Point Dissipation

DOI10.1137/S0363012994269491zbMath0937.93023OpenAlexW1971883113MaRDI QIDQ4883646

S. M. Sun

Publication date: 7 June 2000

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0363012994269491

zbMATH Keywords

existencestabilizationKorteweg-de Vries equationsemigroup theoryexponential decaydissipative boundary conditions

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Stabilization of systems by feedback (93D15) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (12)

Nonhomogeneous boundary value problems for the Korteweg-de Vries equation on a bounded domain ⋮ Control of a Korteweg-de Vries equation: a tutorial ⋮ A non-homogeneous boundary-value problem for the Korteweg-de Vries equation in a quarter plane ⋮ Stability properties of non-constant stationary solutions of the periodic korteweg-de vries Equation ⋮ A Nonhomogeneous Boundary-Value Problem for the Korteweg–de Vries Equation Posed on a Finite Domain ⋮ Qualitative analysis of the dynamic for the nonlinear Korteweg-de Vries equation with a boundary memory ⋮ A Korteweg-de Vries type of fifth-order equations on a finite domain with point dissipation ⋮ A non-homogeneous boundary-value problem for the Korteweg-de Vries equation posed on a finite domain. II. ⋮ Exponential stability for the generalized Korteweg-de Vries equation in a finite interval with weak damping ⋮ Nonlinear Schrödinger equations on a finite interval with point dissipation ⋮ Well-posedness and stability results for the Korteweg-de Vries-Burgers and Kuramoto-Sivashinsky equations with infinite memory: a history approach ⋮ Asymptotic stability of a nonlinear Korteweg-de Vries equation with critical lengths

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