Geodesic
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, Tome 19 (2013) no. 2, pp. 358-384

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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].

DOI : 10.1051/cocv/2012012
Classification : 35Q53
Keywords: The kortweg-de Vries equation, well-posedness, non-homogeneous boundary value problem 
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     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},
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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, Tome 19 (2013) no. 2, pp. 358-384. doi: 10.1051/cocv/2012012

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