Global well-posedness and exponential decay rates for a KdV–Burgers equation with indefinite damping

M.M. Cavalcanti; V.N. Domingos Cavalcanti; V. Komornik; J.H. Rodrigues

doi:10.1016/j.anihpc.2013.08.003

JournalsaihpcVol. 31, No. 5pp. 1079–1100

Global well-posedness and exponential decay rates for a KdV–Burgers equation with indefinite damping

M.M. Cavalcanti
Departamento de Matemática, Universidade Estadual de Maringá, 87020-900, Maringá, PR, Brazil
V.N. Domingos Cavalcanti
Departamento de Matemática, Universidade Estadual de Maringá, 87020-900, Maringá, PR, Brazil
V. Komornik
Département de Mathématique, Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg Cedex, France
J.H. Rodrigues
Departamento de Matemática, Universidade Estadual de Maringá, 87020-900, Maringá, PR, Brazil

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Abstract

We consider the KdV–Burgers equation $u_{t} + u_{xxx} - u_{xx} + λ u + u u_{x} = 0$ and its linearized version $u_{t} + u_{xxx} - u_{xx} + λ u = 0$ on the whole real line. We investigate their well-posedness their exponential stability when $λ$ is an indefinite damping.

Cite this article

M.M. Cavalcanti, V.N. Domingos Cavalcanti, V. Komornik, J.H. Rodrigues, Global well-posedness and exponential decay rates for a KdV–Burgers equation with indefinite damping. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 5, pp. 1079–1100

DOI 10.1016/J.ANIHPC.2013.08.003