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 ∈ H0,ω ∩ H0,ω, where ω ∈ (1/2, 3/2), then there exists a unique solution u ∈ C ([0,∞), H1,ω) of the initial-boundary value problem (0.1). Moreover if the initial data are such that x1+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.
- Dissipative Nonlinear Evolution Equation
- Korteweg-de Vries-Burgers equation
- Large Time Asymptotics
ASJC Scopus subject areas
- Mathematics (miscellaneous)