Korteweg-de Vries-Burgers equation on a half-line with large initial data

We study the following initial-boundary value problem for the Korteweg-de Vries-Burgers equation equation presented We prove that if the initial data u₀ ∈ H^0,ω ∩ H^0,ω, where ω ∈ (1/2, 3/2), then there exists a unique solution u ∈ C ([0,∞), H^1,ω) of the initial-boundary value problem (0.1). Moreover if the initial data are such that x^1+μu₀(x) ∈ L¹, μ = ω - 1/2, then there exists a constant A such that the solution has the following asymptotics equation presented for t → ∞ uniformly with respect to x > 0.