Unique continuation and decay for the Korteweg-de Vries equation with localized damping
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Publication:3365410
DOI10.1051/cocv:2005015zbMath1148.35348OpenAlexW1985982935MaRDI QIDQ3365410
Publication date: 23 January 2006
Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=COCV_2005__11_3_473_0
Asymptotic behavior of solutions to PDEs (35B40) KdV equations (Korteweg-de Vries equations) (35Q53) Continuation and prolongation of solutions to PDEs (35B60)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Uniqueness and non-uniqueness in the Cauchy problem
- Compact sets in the space \(L^ p(0,T;B)\)
- Unique continuation for some evolution equations
- Exponential stabilization of a coupled system of Korteweg-de Vries equations with localized damping.
- Exact boundary controllability of a nonlinear KdV equation with critical lengths
- Unique continuation for weak solutions of the wave equation plus a potential
- Energy decay rates for the von Kármán system of thermoelastic plates
- Exact boundary controllability for the Korteweg-de Vries equation on a bounded domain
- Exponential Decay for The Semilinear Wave Equation with Locally Distributed Damping
- Weak and Strong Interactions between Internal Solitary Waves
- GENERALIZED SOLUTIONS OF THE CAUCHY PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION
- Unique Continuation for the Korteweg–de Vries Equation
- Exact Boundary Controllability of the Korteweg--de Vries Equation
- Stabilization of the Korteweg-de Vries equation with localized damping
- Stabilization and control for the subcritical semilinear wave equation