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Computation of bifurcated branches in a free boundary problem arising in combustion theory

Olivier Baconneau; Claude-Michel Brauner; Alessandra Lunardi — 2000

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Computation of bifurcated branches in a free boundary problem arising in combustion theory

Olivier Baconneau; Claude-Michel Brauner; Alessandra Lunardi — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a parabolic Free Boundary Problem, with jump conditions at the interface. Its planar travelling-wave solutions are orbitally stable provided the bifurcation parameter $u_{*}$ does not exceed a critical value $u_{*}^{c}$ . The latter is the limit of a decreasing sequence $(u_{*}^{k})$ of bifurcation points. The paper deals with the study of the bifurcated branches from the planar branch, for small . Our technique is based on the elimination of the unknown front, turning the problem into a one, to which...

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