Exact boundary controllability of a nonlinear KdV equation with critical lengths

Jean-Michel Coron; Emmanuelle Crépeau

Journal of the European Mathematical Society (2004)

  • Volume: 006, Issue: 3, page 367-398
  • ISSN: 1435-9855

Abstract

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We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.

How to cite

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Coron, Jean-Michel, and Crépeau, Emmanuelle. "Exact boundary controllability of a nonlinear KdV equation with critical lengths." Journal of the European Mathematical Society 006.3 (2004): 367-398. <http://eudml.org/doc/277474>.

@article{Coron2004,
abstract = {We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.},
author = {Coron, Jean-Michel, Crépeau, Emmanuelle},
journal = {Journal of the European Mathematical Society},
keywords = {controllability; nonlinearity; Korteweg-de Vries; controllability of the KdV equation; linear and nonlinear KdV equation; linearization},
language = {eng},
number = {3},
pages = {367-398},
publisher = {European Mathematical Society Publishing House},
title = {Exact boundary controllability of a nonlinear KdV equation with critical lengths},
url = {http://eudml.org/doc/277474},
volume = {006},
year = {2004},
}

TY - JOUR
AU - Coron, Jean-Michel
AU - Crépeau, Emmanuelle
TI - Exact boundary controllability of a nonlinear KdV equation with critical lengths
JO - Journal of the European Mathematical Society
PY - 2004
PB - European Mathematical Society Publishing House
VL - 006
IS - 3
SP - 367
EP - 398
AB - We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.
LA - eng
KW - controllability; nonlinearity; Korteweg-de Vries; controllability of the KdV equation; linear and nonlinear KdV equation; linearization
UR - http://eudml.org/doc/277474
ER -

Citations in EuDML Documents

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  1. Ademir Fernando Pazoto, Unique continuation and decay for the Korteweg-de Vries equation with localized damping
  2. Ademir Fernando Pazoto, Unique continuation and decay for the Korteweg-de Vries equation with localized damping
  3. Carlos F. Vasconcellos, Patricia N. da Silva, Stabilization of the Kawahara equation with localized damping
  4. Karine Beauchard, Controllability of Schrödinger equations
  5. Carlos F. Vasconcellos, Patricia N. da Silva, Stabilization of the Kawahara equation with localized damping
  6. Eduardo Cerpa, Emmanuelle Crépeau, Boundary controllability for the nonlinear Korteweg-de Vries equation on any critical domain
  7. O. Glass, S. Guerrero, On the controllability of the fifth-order Korteweg-de Vries equation
  8. Ciro D'Apice, Umberto De Maio, Peter I. Kogut, Suboptimal boundary controls for elliptic equation in critically perforated domain
  9. Karine Beauchard, Controllability of a quantum particle in a 1D variable domain
  10. Eugene Kramer, Ivonne Rivas, Bing-Yu Zhang, Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain

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