Korteweg–de Vries–Burgers system in

We study Cauchy problem in R N for the Korteweg–de Vries–Burgers system. Parabolic regularization technique is used to prove its global in time solvability. The regularization effect of the Laplacian term is observed for the viscous solutions constructed in the paper. Asymptotic behavior of weak solutions is discussed next in the language of the global attractors.