Decay of Solutions to Damped Korteweg–de Vries Type Equation

Decay of Solutions to Damped Korteweg–de Vries Type Equation In the present paper we establish results concerning the decay of the energy related to the damped Korteweg–de Vries equation posed on infinite domains. We prove the exponential decay rates of the energy when a initial value problem and a localized dissipative mechanism are in place. If this mechanism is effective in the whole line, we get a similar result in H k -level, k ∈ℕ. In addition, the decay of the energy regarding a initial boundary value problem posed on the right half-line, is obtained considering convenient a smallness condition on the initial data but a more general dissipative effect. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Decay of Solutions to Damped Korteweg–de Vries Type Equation

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Publisher
Springer-Verlag
Copyright
Copyright © 2012 by Springer Science+Business Media, LLC
Subject
Mathematics; Numerical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-011-9156-7
Publisher site
See Article on Publisher Site

Abstract

In the present paper we establish results concerning the decay of the energy related to the damped Korteweg–de Vries equation posed on infinite domains. We prove the exponential decay rates of the energy when a initial value problem and a localized dissipative mechanism are in place. If this mechanism is effective in the whole line, we get a similar result in H k -level, k ∈ℕ. In addition, the decay of the energy regarding a initial boundary value problem posed on the right half-line, is obtained considering convenient a smallness condition on the initial data but a more general dissipative effect.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Apr 1, 2012

References

  • Well-posedness and scattering results for the generalized Korteweg–de Vries equation via the contraction principle
    Kenig, C.E.; Ponce, G.; Vega, L.
  • Modified KdV equation with a source term in a bounded domain
    Larkin, N.A.

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