Xavier Carvajal, Mahendra Panthee
Abstract:
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.
Submitted September 9, 2011. Published March 14, 2012.
Math Subject Classifications: 35A07, 35Q53.
Key Words: Initial value problem; well-posedness; Bourgain spaces,
KdV equation.
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Xavier Carvajal Instituto de Matemática - UFRJ Av. Horácio Macedo Centro de Tecnologia Cidade Universitária, Ilha do Fundão Caixa Postal 68530, 21941-972 Rio de Janeiro, RJ, Brasil email: carvajal@im.ufrj.br |
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Mahendra Panthee Centro de Matemática Universidade do Minho 4710-057, Braga, Portugal email: mpanthee@math.uminho.pt |
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