Global well-posedness and exponential decay rates for a KdV–Burgers equation with indefinite damping
Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 5, p. 1079-1100

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

DOI : https://doi.org/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--Burgers equation with indefinite damping},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {31},
     number = {5},
     year = {2014},
     pages = {1079-1100},
     doi = {10.1016/j.anihpc.2013.08.003},
     zbl = {1302.35332},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2014__31_5_1079_0}
}
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, Volume 31 (2014) no. 5, pp. 1079-1100. doi : 10.1016/j.anihpc.2013.08.003. http://www.numdam.org/item/AIHPC_2014__31_5_1079_0/

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