Regularity near a contact point for flame propagation

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study a free boundary problem, arising from a model for the propagation of laminar flames. Consider a cylindrical region S in IRn, and the following free boundary problem with Dirichlet data on ∂S: ut=Δu in {u>0} ∩S, |Δu|=1 on ∂ {u>0} ∩S and u=0 on ∂S. We show that if there is a contact point of the free boundary {u=0, |Δu|=1} with ∂S, then the free boundary approaches ∂S tangentially and it turns out to be a graph of C1+α,α function near the contact point. In particular, the space normal is Hölder continuous.

Original languageEnglish (US)
Pages (from-to)457-474
Number of pages18
JournalCommunications in Partial Differential Equations
Volume34
Issue number5
DOIs
StatePublished - May 1 2009

Keywords

  • Combustion
  • Contact point
  • Free-boundary problem
  • Heat equation
  • Regularity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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