In this paper, we study a class of Initial-Boundary Value Problems proposed by Colin and Ghidaglia for the Korteweg-de Vries equation posed on a bounded domain (0,L). We show that this class of Initial-Boundary Value Problems is locally well-posed in the classical Sobolev space Hs(0,L) for s > -3/4, which provides a positive answer to one of the open questions of Colin and Ghidaglia [Adv. Differ. Equ. 6 (2001) 1463-1492].
Keywords: The kortweg-de Vries equation, well-posedness, non-homogeneous boundary value problem
@article{COCV_2013__19_2_358_0, author = {Kramer, Eugene and Rivas, Ivonne and Zhang, Bing-Yu}, title = {Well-posedness of a class of non-homogeneous boundary value problems of the {Korteweg-de} {Vries} equation on a finite domain}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {358--384}, publisher = {EDP-Sciences}, volume = {19}, number = {2}, year = {2013}, doi = {10.1051/cocv/2012012}, mrnumber = {3049715}, zbl = {1273.35238}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2012012/} }
TY - JOUR AU - Kramer, Eugene AU - Rivas, Ivonne AU - Zhang, Bing-Yu TI - Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2013 SP - 358 EP - 384 VL - 19 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2012012/ DO - 10.1051/cocv/2012012 LA - en ID - COCV_2013__19_2_358_0 ER -
%0 Journal Article %A Kramer, Eugene %A Rivas, Ivonne %A Zhang, Bing-Yu %T Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 358-384 %V 19 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2012012/ %R 10.1051/cocv/2012012 %G en %F COCV_2013__19_2_358_0
Kramer, Eugene; Rivas, Ivonne; Zhang, Bing-Yu. Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 2, pp. 358-384. doi : 10.1051/cocv/2012012. http://www.numdam.org/articles/10.1051/cocv/2012012/
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