Global stability of strong rarefaction waves for the generalized KdV-Burgers equation (Q867833)

The authors deal with the global stability of strong rarefaction waves of the Cauchy problem for the generalized KdV-Burgers equation, \[ u_t+f(u)_x=\mu u_{xx}+\delta u_{xxx},\;\mu >0,\;\delta\in{\mathbb R} \] with initial data \(u(x,t)| _{t=0}=u_0(x)\rightarrow u{\pm}, x\rightarrow\pm\infty.\) In contrast to former results obtained by \textit{Z. Wang} and \textit{C. J. Zhu} [Acta Math. Sci., Ser. B, Engl. Ed. 22, No. 3, 319--328 (2002; Zbl 1003.35111)], the strength of the rarefaction waves to be small is not required here, and the initial disturbance can also be chosen large.