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. © Springer Science+Business Media, LLC 2011.

Authors
Cavalcanti M.M.1 , Cavalcanti V.N.D.1 , Faminskii A. 2 , Natali F.1
Editors
-
Publisher
-
Number of issue
2
Language
English
Pages
221-251
Status
Published
Department
-
Number
-
Volume
65
Year
2012
Organizations
  • 1 Department of Mathematics, State University of Maringá, Avenida Colombo, 5790, CEP 87020-900, Maringá, PR, Brazil
  • 2 Faculty of Science, Peoples' Friendship University of Russia, Miklukho-Maklai str. 6, Moscow, 117198, Russian Federation
Keywords
Decay of solutions; Dissipative mechanism; Korteweg-de Vries equation; Localized damping
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/2332/