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Decay of Solutions to Damped Korteweg–de Vries Type Equation

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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.

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Authors and Affiliations

  1. Department of Mathematics, State University of Maringá, Avenida Colombo, 5790, CEP 87020-900, Maringá, PR, Brazil

    Marcelo M. Cavalcanti, Valéria N. Domingos Cavalcanti & Fábio Natali

  2. Faculty of Science, Peoples’ Friendship University of Russia, Miklukho-Maklai str. 6, Moscow, 117198, Russia

    Andrei Faminskii

Authors
  1. Marcelo M. Cavalcanti
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  2. Valéria N. Domingos Cavalcanti
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  3. Andrei Faminskii
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  4. Fábio Natali
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Correspondence to Marcelo M. Cavalcanti.

Additional information

Research of M.M. Cavalcanti partially supported by the CNPq, grant 300631/2003-0.

Research of V.N. Domingos Cavalcanti partially supported by the CNPq, grant 304895/2003-2.

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Cavalcanti, M.M., Domingos Cavalcanti, V.N., Faminskii, A. et al. Decay of Solutions to Damped Korteweg–de Vries Type Equation. Appl Math Optim 65, 221–251 (2012). https://doi.org/10.1007/s00245-011-9156-7

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