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On the well-posedness and large-time behavior of higher order Boussinesq system

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Published 15 April 2019 • © 2019 IOP Publishing Ltd & London Mathematical Society
, , Citation Roberto A Capistrano-Filho et al 2019 Nonlinearity 32 1852 DOI 10.1088/1361-6544/aafe34

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Author e-mails

capistranofilho@dmat.ufpe.br

roberto.capistranofilho@ufpe.br

fagallegor@unal.edu.co

ferangares@gmail.com

ademir@im.ufrj.br

Author affiliations

1 Departamento de Matemática, Universidade Federal de Pernambuco (UFPE), 50740-545, Recife (PE), Brazil

2 Departamento de Matemáticas, Universidad Nacional de Colombia, UNAL, Cra 27 No. 64-60, 170003, Manizales, Colombia

3 Institute of Mathematics, Federal University of Rio de Janeiro (UFRJ), PO Box 68530, CEP 21945-970, Rio de Janeiro (RJ), Brazil

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Dates

  1. Received 28 August 2018
  2. Accepted 14 January 2019
  3. Published

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0951-7715/32/5/1852

Abstract

A family of Boussinesq systems has been proposed to describe the bi-directional propagation of small amplitude long waves on the surface of shallow water. In this paper, we investigate the well-posedness and boundary stabilization of the generalized higher order Boussinesq systems of Korteweg–de Vries—type posed on a interval. We design a two-parameter family of feedback laws for which the system is locally well-posed and the solutions of the linearized system are exponentially decreasing in time.

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10.1088/1361-6544/aafe34