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

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

doi:10.1016/j.anihpc.2013.08.003

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

Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 5, pp. 1079-1100

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Résumé

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

Zbl

DOI : 10.1016/j.anihpc.2013.08.003

Classification : 35Q53, 93D15
Keywords: KdV–Burgers equation, Well-posedness, Stabilization by feedback, Decay rate

@article{AIHPC_2014__31_5_1079_0,
     author = {Cavalcanti, M.M. and Domingos Cavalcanti, V.N. and Komornik, V. and Rodrigues, J.H.},
     title = {Global well-posedness and exponential decay rates for a {KdV{\textendash}Burgers} equation with indefinite damping},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1079--1100},
     publisher = {Elsevier},
     volume = {31},
     number = {5},
     year = {2014},
     doi = {10.1016/j.anihpc.2013.08.003},
     zbl = {1302.35332},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2013.08.003/}
}

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Cavalcanti, M.M.; Domingos Cavalcanti, V.N.; Komornik, V.; Rodrigues, J.H. Global well-posedness and exponential decay rates for a KdV–Burgers equation with indefinite damping. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 5, pp. 1079-1100. doi: 10.1016/j.anihpc.2013.08.003

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