Korteweg-de Vries-Burgers equation on a segment

Elena I. Kaikina; Leonardo Guardado-Zavala; Hector F. Ruiz-Paredes; S. Juarez Zirate

doi:10.4067/S0719-06462010000100005

Authors

Elena I. Kaikina Instituto de Matemáticas, UNAM Campus Morelia, AP 61-3 (Xangari), Morelia CP 58089, Michoacán, México.
Leonardo Guardado-Zavala Posgrado Eléctrica, Instituto Tecnológico de Morelia, CP 58120, Morelia, Michoacán, México.
Hector F. Ruiz-Paredes Posgrado Eléctrica, Instituto Tecnológico de Morelia, CP 58120, Morelia, Michoacán, México.
S. Juarez Zirate Posgrado Eléctrica, Instituto Tecnológico de Morelia, CP 58120, Morelia, Michoacán, México.

DOI:

https://doi.org/10.4067/S0719-06462010000100005

Keywords:

Dissipative Nonlinear Evolution Equation, Large Time Asymptotics, Korteweg-de Vries-Burgers equation

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 âˆˆ L², then there exists a unique solution u âˆˆ C ([0, âˆž) ; L²) âˆª C ((0,âˆž) ; H¹) of the initial-boundary value problem (0.1). We also obtain the large time asymptotic of solution uniformly with respect to x âˆˆ (0, 1) as t â†’ âˆž.