Global well-posedness and inviscid limit for the modified Korteweg-de Vries-Burgers equation

Considering the Cauchy problem for the modified Korteweg-de Vries-Burgers equation u(t) + u(xxx) + epsilon vertical bar partial derivative(x)vertical bar(2 alpha)u = 2(u(3))(x), u(0) = phi where 0 < epsilon, alpha <= 1 and u is a real-valued function, we show that it is uniformly globally well-posed in H-s (s >= 1) for all epsilon is an element of (0, 1]. Moreover, we prove that for any s >= 1 and T > 0, its solution converges in C ([0, T]; H-s) to that of the MKdV equation if epsilon tends to 0. (C) 2009 Elsevier Ltd. All rights reserved.