Journal of Geometric Analysis

, Volume 18, Issue 4, pp 1098–1126 | Cite as

Nonuniqueness in a Free Boundary Problem from Combustion

  • Arshak Petrosyan
  • Nung Kwan Yip


We study a parabolic free boundary problem with a fixed gradient condition which serves as a simplified model for the propagation of premixed equidiffusional flames. We give a rigorous justification of an example due to J.L. Vázquez that the initial data in the form of two circular humps leads to the nonuniqueness of limit solutions if the supports of the humps touch at the time of their maximal expansion.


Nonuniqueness Free boundary problem Singular perturbations Flame propagation Combustion 

Mathematics Subject Classification (2000)

35R35 35K57 80A22 80A25 


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© Mathematica Josephina, Inc. 2008

Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA

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