The goal of this paper is to prove the existence, uniqueness and the energy decay of global regular solutions of the KdV equation in a bounded domain approximating it by the Kuramoto-Sivashinsky equations.
@article{7493, title = {Korteweg-de Vries Equation in Bounded Domains - doi: 10.5269/bspm.v22i1.7493}, journal = {Boletim da Sociedade Paranaense de Matem\'atica}, volume = {23}, year = {2009}, doi = {10.5269/bspm.v22i1.7493}, language = {EN}, url = {http://dml.mathdoc.fr/item/7493} }
Larkin, Nikolai A. Korteweg-de Vries Equation in Bounded Domains - doi: 10.5269/bspm.v22i1.7493. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v22i1.7493. http://gdmltest.u-ga.fr/item/7493/