(untitled) (Journal of Partial Differential Equations, 2003)
" 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) 2229 L^221e(0, T; dotH^-s)(0 2264 s < 1) are obtained for initial data in dotH^-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 equality, so the initial data can be arbitrarily large to obtain the global solution."