Korteweg-de Vries-Burgers equation on a segment

Abstract

We study the following initial-boundary value problem for the Korteweg-de Vries-Burgers equation on the interval (0, 1)

We prove that if the initial data u₀ ∈ L², then there exists a unique solution u ∈ C ([0, ∞) ; L²) ∪ C ((0,∞) ; H¹) of the initial-boundary value problem (0.1). We also obtain the large time asymptotic of solution uniformly with respect to x ∈ (0, 1) as t → âˆž.