GLOBAL STEADY-STATE STABILIZATION AND CONTROLLABILITY OF 1D SEMILINEAR WAVE EQUATIONS

@article{Coron2006GLOBALSS,
  title={GLOBAL STEADY-STATE STABILIZATION AND CONTROLLABILITY OF 1D SEMILINEAR WAVE EQUATIONS},
  author={J. Coron and E. Tr{\'e}lat},
  journal={Communications in Contemporary Mathematics},
  year={2006},
  volume={08},
  pages={535-567}
}
This paper is concerned with the exact boundary controllability of semilinear wave equations in one space dimension. We prove that it is possible to move from any steady-state to any other one by means of a boundary control, provided that they are in the same connected component of the set of steady-states. The proof is based on an expansion of the solution in a one-parameter Riesz basis of generalized eigenvectors, and on an effective feedback stabilization procedure which is implemented. 

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References

SHOWING 1-10 OF 33 REFERENCES
Global steady-state controllability of 1-D semilinear heat equations
Global Steady-State Controllability of One-Dimensional Semilinear Heat Equations
Exact Controllability for Semilinear Wave Equations
Exact controllability in "arbitrarily short time" of the semilinear wave equation
Well posedness and control of semilinear wave equations with iterated logarithms
Local controllability of a 1-D Schrödinger equation
Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations
RAPID BOUNDARY STABILIZATION OF LINEAR DISTRIBUTED SYSTEMS
...
1
2
3
4
...