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Initial boundary value problems for some nonlinear dispersive models on the half-line: a review and open problems

  • Special Section: Nonlinear Dispersive Equations
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Abstract

In the last years the study of initial boundary value problems for nonlinear dispersive equations on the half-lines has given attention of many researchers. This turns out to be a rather challenging problem, mainly when studied in low Sobolev regularity. In this note we present a review of the main results about this topic and also introduce interesting open problems which still requires attention from the mathematical point of view.

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Acknowledgements

The author thanks the commit organizer for the invitation, hospitality and financial support to Third workshop on nonlinear dispersive equations at Campinas-Brazil. The author also wish to thank the referee for a careful reading and helpful suggestions.

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  1. Instituto de Matemática, Universidade Federal de Alagoas, Maceió, AL, 50740-545, Brazil

    Márcio Cavalcante

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Cavalcante, M. Initial boundary value problems for some nonlinear dispersive models on the half-line: a review and open problems. São Paulo J. Math. Sci. 13, 418–434 (2019). https://doi.org/10.1007/s40863-019-00144-5

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