Polynomial representations for initial-boundary value problems involving the inviscid Proudman-Johnson equation

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Abstract

The central aim of this paper is to show how two-point Hermite interpolation can be used to construct polynomial representations of solutions to some initial-boundary-value problems for the inviscid Proudman-Johnson equation. This classic equation of fluid dynamics can be regarded as first-order hyperbolic, and an important by-product of our analysis is an understanding of how Hermite interpolation can be utilized for such equations. Different types of boundary conditions may result in finite time blow-up and/or large time approach to the steady state depending on the value of a parameter appearing in the problem.

Original languageEnglish
Pages (from-to)631-650
Number of pages20
JournalQuarterly Journal of Mechanics & Applied Mathematics
Volume59
Issue number4
DOIs
Publication statusPublished - Nov 2006

Keywords

  • BLOW-UP
  • STAGNATION-POINT
  • FLOW

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