Moving boundary value problems for the wave equation

Beatrice Pelloni, Dimitrios Pinotsis

Research output: Contribution to journalArticle

Abstract

We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework.
Original languageEnglish
Pages (from-to)1685-1691
Number of pages7
JournalJournal of Computational and Applied Mathematics
Volume234
Issue number6
DOIs
Publication statusPublished - 15 Jul 2010

Keywords

  • Boundary value problems
  • Riemann–Hilbert problems
  • Moving boundary
  • Wave equation

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