The boundary control of MKdV_Burgers equation was considered by feedback control on the domain[0,1].The existence of the solution of MKdV_Burgers equation with the feedback control law was proved.On the base,priori estimates for the solution was given.At last,the existence of the weak solution of MKdV_Burgers equation was proved and global_exponential and asymptotic stability of the solution of MKdV_Burgers equation was given.
Russell D L,Zhang B Y.Exact controllability and stabilizability of the Korteweg-de Vries equation[J].Trans Amer Math,1996,348(9):3643—3672. doi: 10.1090/S0002-9947-96-01672-8
[2]
Naumkin P I,Shishmarev I A.On the decay of step-like data for the Korteweg-de-Vries-Burgers equation[J].Funktsional.Anal.Prilozhen,1992,26(2):88—93.
[3]
LIU Wei-jiu,Miroslav Krstic.Global boundary stabilization of the Korteweg-de Vries Burgers equation[J].Computational and Applied Math,2002,21(1):315—354.