The Role of Periodicity in the Solution of Third Order Boundary Value Problems

Beatrice Pelloni, David Smith

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review


In this short paper, we elucidate how the solution of certain illustrative boundary value problems for the Airy equation 𝑢𝑡+𝑢𝑥𝑥𝑥=0 on [0, 1] can be expressed as a perturbation of the solution of the purely periodic problem. The motivation is to understand the role boundary conditions play in the properties of the solution. This is particularly important in related work on the solution of linear dispersive problems with discontinuous initial data and the phenomena of revivals and fractalization.
Original languageEnglish
Title of host publicationChaos, Fractals and Complexity
EditorsTassos Bountis, Filippos Vallianatos, Astero Provata, Dimitris Kugiumtzis, Yannis Kominis
Number of pages13
ISBN (Electronic)9783031374043
ISBN (Print)9783031374036, 9783031374067
Publication statusPublished - 22 Sept 2023

Publication series

NameSpringer Proceedings in Complexity
ISSN (Print)2213-8684
ISSN (Electronic)2213-8692


  • Fokas transform method
  • Initial boundary value problems
  • Regularity of solutions
  • Revivals and fractalization

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Modelling and Simulation


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