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

Olivier Baconneau; Claude-Michel Brauner; Alessandra Lunardi

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2000)

  • Volume: 34, Issue: 2, page 223-239
  • ISSN: 0764-583X

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Baconneau, Olivier, Brauner, Claude-Michel, and Lunardi, Alessandra. "Computation of bifurcated branches in a free boundary problem arising in combustion theory." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 34.2 (2000): 223-239. <http://eudml.org/doc/193984>.

@article{Baconneau2000,
author = {Baconneau, Olivier, Brauner, Claude-Michel, Lunardi, Alessandra},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {free boundary problem; travelling-wave solutions; bifurcation points; bifurcated branches; arc length continuation},
language = {eng},
number = {2},
pages = {223-239},
publisher = {Dunod},
title = {Computation of bifurcated branches in a free boundary problem arising in combustion theory},
url = {http://eudml.org/doc/193984},
volume = {34},
year = {2000},
}

TY - JOUR
AU - Baconneau, Olivier
AU - Brauner, Claude-Michel
AU - Lunardi, Alessandra
TI - Computation of bifurcated branches in a free boundary problem arising in combustion theory
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2000
PB - Dunod
VL - 34
IS - 2
SP - 223
EP - 239
LA - eng
KW - free boundary problem; travelling-wave solutions; bifurcation points; bifurcated branches; arc length continuation
UR - http://eudml.org/doc/193984
ER -

References

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  1. [1] O. Baconneau, Bifurcation de fronts pour un problème à frontière libre en combustion. Ph.D. thesis, Université Bordeaux 1 (1998). 
  2. [2] C.-M. Brauner, J. Hulshof and A. Lunardi, A general approach to stability in free boundary problems. J. Differential Equations (to appear). Zbl0973.35200
  3. [3] C.-M. Brauner and A. Lunardi, Bifurcation of nonplanar travelling waves in a free boundary problem. Nonlinear Analysis T. M. A. (to appear). Zbl0981.35102MR1816662
  4. [4] C.-M. Brauner, A. Lunardi and Cl. Schmidt-Lainé, Stability of travelling waves with interface conditions. Nonlinear Analysis T. M. A. 19 (1992) 465-484. Zbl0780.35115MR1181348
  5. [5] C.-M. Brauner, A. Lunardi and Cl. Schmidt-Lainé, Multidimensional stability analysis of planar travelling waves. Appl. Math, Lett. 7 (1994) 1-4. Zbl0814.35148MR1350600
  6. [6] C.-M. Brauner, A. Lunardi and Cl. Schmidt-Lainé, Stability of travelling waves in a multidimensional free boundary problem. Nonlinear Analysis T.M.A. (to appear). Zbl1032.35082MR1816663
  7. [7] M.G. Crandall and P.H. Rabinowitz, Bifurcation from simple eigenvalues. J. Funct. Anal. 8 (1971) 321-340. Zbl0219.46015MR288640
  8. [8] H.B. Keller, Numerical solution of bifurcation and non linear eigenvalue problems. P. Rabinowitz Ed., Academic Press, New York (1978) 73-94. 
  9. [9] D.H. Sattinger, Stability of waves of nonlinear parabolic equations. Adv. Math. 22 (1976) 141-178. Zbl0344.35051MR435602
  10. [10] D.S. Stewart and G.S.S. Ludford, The acceleration of fast deflagration waves. Z.A.M.M. 63 (1983) 291-302. Zbl0564.76110
  11. [11] J.L. Vazquez, The Free Boundary Problem for the Heat Equation with fixed Gradient Condition, Proc. Int. Conf. "Free Boundary Problem and Applications", Zakopane, Pitman Res. Notes Math. 363, Longman (1996). Zbl0867.35120MR1462990

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