# Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain

Eugene Kramer; Ivonne Rivas; Bing-Yu Zhang

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 2, page 358-384
- ISSN: 1292-8119

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topKramer, Eugene, Rivas, Ivonne, and 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 19.2 (2013): 358-384. <http://eudml.org/doc/272905>.

@article{Kramer2013,

abstract = {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].},

author = {Kramer, Eugene, Rivas, Ivonne, Zhang, Bing-Yu},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {The kortweg-de Vries equation; well-posedness; non-homogeneous boundary value problem; KdV; well posedness, non-homogeneous boundary value problems},

language = {eng},

number = {2},

pages = {358-384},

publisher = {EDP-Sciences},

title = {Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain},

url = {http://eudml.org/doc/272905},

volume = {19},

year = {2013},

}

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

PB - EDP-Sciences

VL - 19

IS - 2

SP - 358

EP - 384

AB - 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].

LA - eng

KW - The kortweg-de Vries equation; well-posedness; non-homogeneous boundary value problem; KdV; well posedness, non-homogeneous boundary value problems

UR - http://eudml.org/doc/272905

ER -

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