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 → ∞.
@article{1425,
title = {Korteweg-de Vries-Burgers Equation on a Segment},
journal = {CUBO, A Mathematical Journal},
volume = {12},
year = {2010},
language = {en},
url = {http://dml.mathdoc.fr/item/1425}
}
Kaikina, Elena I.; Guardado-Zavala, Leonardo; Ruiz-Paredes, Hector F.; Juarez Zirate, S. Korteweg-de Vries-Burgers Equation on a Segment. CUBO, A Mathematical Journal, Tome 12 (2010) . http://gdmltest.u-ga.fr/item/1425/