Abstract
Bifurcating solution branches and their numerical approximations of a semi-linear elliptic problem are considered at corank-2 bifurcaton points. Utilization of basic group concepts allows a classification of the solution curves with their symmetries, and in turn, leads to reductions of singularity of the problem at bifurcation points and computational work in path following of solution branches.
Zusammenfassung
Abzweigende Lösungskurven und deren numerische Behandlung bei eine semilinearen elliptischen Problem werden bei Korang-2 Verzweigungspunkten diskutiert. Einige, Grundideen der Gruppentheorie erlauben eine Klassifizierung der abzweigenden Lösungskurven nach ihren Symmetrien, sowie eine Reduktion der Siingularität des Problems bei Verzweigungspunkten und eine Reduktion des Rechenaufwand in der Verfolgerung der Lösungskurven.
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The work was supported by the Deutsche Forschungsgemeinschaft.
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Mei, Z. Path following around corank-2 bifurcation pints of a semi-linear elliptic problem with symmetry. Computing 47, 69–85 (1991). https://doi.org/10.1007/BF02242023
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DOI: https://doi.org/10.1007/BF02242023