Regularity near a contact point for flame propagation

Sunhi Choi

doi:10.1080/03605300902740387

Regularity near a contact point for flame propagation

Sunhi Choi

Research output: Contribution to journal › Article › peer-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 C^1+α,α function near the contact point. In particular, the space normal is Hölder continuous.

Original language	English (US)
Pages (from-to)	457-474
Number of pages	18
Journal	Communications in Partial Differential Equations
Volume	34
Issue number	5
DOIs	https://doi.org/10.1080/03605300902740387
State	Published - May 2009

Keywords

Combustion
Contact point
Free-boundary problem
Heat equation
Regularity

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1080/03605300902740387

Cite this

@article{292058d654de413abf968eb283487bd9,

title = "Regularity near a contact point for flame propagation",

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 H{\"o}lder continuous.",

keywords = "Combustion, Contact point, Free-boundary problem, Heat equation, Regularity",

author = "Sunhi Choi",

note = "Funding Information: The author was partially supported by NSF 0713598.",

year = "2009",

month = may,

doi = "10.1080/03605300902740387",

language = "English (US)",

volume = "34",

pages = "457--474",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor and Francis Ltd.",

number = "5",

}

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

UR - https://www.scopus.com/pages/publications/68949211078

UR - https://www.scopus.com/pages/publications/68949211078#tab=citedBy

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 -

Regularity near a contact point for flame propagation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this