TY - JOUR
T1 - Regularity near a contact point for flame propagation
AU - Choi, Sunhi
N1 - Funding Information:
The author was partially supported by NSF 0713598.
PY - 2009/5
Y1 - 2009/5
N2 - 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.
AB - 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.
KW - Combustion
KW - Contact point
KW - Free-boundary problem
KW - Heat equation
KW - Regularity
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U2 - 10.1080/03605300902740387
DO - 10.1080/03605300902740387
M3 - Article
AN - SCOPUS:68949211078
SN - 0360-5302
VL - 34
SP - 457
EP - 474
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 5
ER -