Geodesic
Well-posedness of KdV type equations
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this work, we study the initial value problems associated to some linear perturbations of KdV equations. Our focus is in the well-posedness issues for initial data given in the L^2-based Sobolev spaces. We develop a method that allows us to treat the problem in the Bourgain's space associated to the KdV equation. With this method, we can use the multilinear estimates developed in the KdV context, thereby getting analogous well-posedness results for linearly perturbed equations.
Classification : 35A07, 35Q53
Keywords: initial value problem, well-posedness, Bourgain spaces, KdV equation 
@article{EJDE_2012__2012__a93,
     author = {Carvajal, Xavier and Panthee, Mahendra},
     title = {Well-posedness of {KdV} type equations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a93/}
}
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Carvajal, Xavier; Panthee, Mahendra. Well-posedness of KdV type equations. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a93/