The generalized Korteweg-de Vries-Burgers equation in H2(R)

The generalized KdV-Burgers equation u(t)+(delta u(xx)+g(u))(x)-nu u(xx)+gamma u = f (x), delta, nu > 0, gamma >= 0, is considered in this paper. Using the parabolic regularization technique we prove local and global solvability in H-2(R) of the Cauchy problem for this equation. Several regularity properties of the approximations stay valid for solutions constructed in such a way. Next, for when gamma > 0, we study the asymptotic behavior of the corresponding semigroup on H-2(R), constructing the (H-2(R), H3- (R)) global attractor. (C) 2010 Elsevier Ltd. All rights reserved.