摘要
The Cauchy problem for the generalized Korteweg-de Vries-Burgers equation is considered and the local existence and uniqueness of solutions in L^q (0, T; L^p)∩L^∞(0,T; H^-s)(0≤ s < 1) are obtained for initial data in H^-s. Moreover, the local solutions are global if the initial data are sufficiently small in critical case. Particularly, for s=0, the generalized Korteweg-de Vries-Burgers equation satisfies the energy eauality, so the initial data can be arbitrarily large to obtain the global solution.
