Detection of high codimensional bifurcations in variational PDEs

L. M. Kreusser, R. I. Mclachlan, C. Offen

Research output: Contribution to journalArticlepeer-review

Abstract

We derive bifurcation test equations for A-series singularities of nonlinear functionals and, based on these equations, we propose a numerical method for detecting high codimensional bifurcations in parameter-dependent PDEs such as parameter-dependent semilinear Poisson equations. As an example, we consider a Bratu-type problem and show how high codimensional bifurcations such as the swallowtail bifurcation can be found numerically. In particular, our original contributions are (1) the use of the Infinite-Dimensional Splitting Lemma, (2) the unified and simplified treatment of all A-series bifurcations, (3) the presentation in Banach spaces, i.e. our results apply both to the PDE and its (variational) discretization, (4) further simplifications for parameter-dependent semilinear Poisson equations (both continuous and discrete), and (5) the unified treatment of the continuous problem and its discretisation.

Original languageEnglish
Pages (from-to)2335-2363
Number of pages29
JournalNonlinearity
Volume33
Issue number5
DOIs
Publication statusPublished - May 2020

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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