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Detection of high codimensional bifurcations in variational PDEs

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GCS - Geometry, compatibility and structure preservation in computational differential equations

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.

Lisa Maria Kreusser, Robert I McLachlan, Christian Offen

This talk is part of the Isaac Newton Institute Seminar Series series.

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