2 results
𝒞1,β regularity for Dirichlet problems associated to fully nonlineardegenerate elliptic equations
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 20 / Issue 4 / October 2014
- Published online by Cambridge University Press:
- 13 August 2014, pp. 1009-1024
- Print publication:
- October 2014
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- Article
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Computation of bifurcated branches in a free boundary problem arising in combustion theory
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- Journal:
- ESAIM: Mathematical Modelling and Numerical Analysis / Volume 34 / Issue 2 / March 2000
- Published online by Cambridge University Press:
- 15 April 2002, pp. 223-339
- Print publication:
- March 2000
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- Article
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We consider a parabolic 2D Free Boundary Problem, with jump conditions at the interface. Its planar travelling-wave solutions are orbitally stableprovided the bifurcation parameter $u_*$
does not exceed a critical value $u_{*}^{c}$ 
. The latter isthe limit of a decreasing sequence $(u_{*}^{k})$ 
of bifurcation points. The paper deals with the study of the 2D bifurcated branchesfrom the planar branch, for small k. Our technique is based on the elimination of the unknown front, turning the problem into a fully nonlinear one, to which we canapply the Crandall-Rabinowitz bifurcation theorem for a local study.We point out that the fully nonlinear reformulation of the FBP can also serve to developefficient numerical schemes in view of global information, such as techniques based on arc length continuation.
