Boundary Value Problems for Boussinesq Type Systems

A. S. Fokas, Beatrice Pelloni

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

We characterise the boundary conditions that yield a linearly well posed problem for the so-called KdV–KdV system and for the classical Boussinesq system. Each of them is a system of two evolution PDEs modelling two-way propagation of water waves. We study these problems with the spatial variable in either the half-line or in a finite interval. The results are obtained by extending a spectral transform approach, recently developed for the analysis of scalar evolution PDEs, to the case of systems of PDEs.
The knowledge of the boundary conditions that should be imposed in order for the problem to be linearly well posed can be used to obtain an integral representation of the solution. This knowledge is also necessary in order to conduct numerical simulations for the fully nonlinear systems.
Original languageEnglish
Pages (from-to)59-96
Number of pages38
JournalMathematical Physics, Analysis and Geometry
Volume8
Issue number1
DOIs
Publication statusPublished - Feb 2005

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