Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Sharp local well-posedness of KdV type equations with dissipative perturbations

Authors: Xavier Carvajal and Mahendra Panthee
Journal: Quart. Appl. Math. 74 (2016), 571-594
MSC (2010): Primary 35A01, 35Q53
DOI: https://doi.org/10.1090/qam/1437
Published electronically: June 16, 2016
MathSciNet review: 3518228
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Abstract: In this work, we study the initial value problems associated to some linear perturbations of the KdV equation. Our focus is on the well-posedness issues for initial data given in the $ L^2$-based Sobolev spaces. We derive a bilinear estimate in a space with weight in the time variable and obtain sharp local well-posedness results.

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Xavier Carvajal
Affiliation: Instituto de Matemática - UFRJ, Av. Horácio Macedo, Centro de Tecnologia, Cidade Universitária, Ilha do Fundão, 21941-972 Rio de Janeiro, RJ, Brazil
Email: carvajal@im.ufrj.br

Mahendra Panthee
Affiliation: Departamento de Matemática - UNICAMP, R. Sergio Buarque de Holanda 651, 13083-859, Campinas, SP, Brazil
Email: mpanthee@ime.unicamp.br

DOI: https://doi.org/10.1090/qam/1437
Keywords: Initial value problem, well-posedness, KdV equation, dispersive-dissipative models
Received by editor(s): October 19, 2015
Published electronically: June 16, 2016
Article copyright: © Copyright 2016 Brown University

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