Journal
NONLINEARITY
Volume 30, Issue 5, Pages 1853-1875Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1361-6544/aa64e7
Keywords
Aubry-Mather theory; effective Hamiltonian; effective burning velocity; flame propagation; viscosity solutions; weak KAM theory
Categories
Funding
- NSF [DMS-1515150, DMS-1615944]
- NSF CAREER [DMS-1151919]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1515150] Funding Source: National Science Foundation
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The main goal of this paper is to understand finer properties of the effective burning velocity from a combustion model introduced by Majda and Souganidis (1994 Nonlinearity 7 1-30). Motivated by results in Bangert (1994 Calculus Variations PDE 2 49-63) and applications in turbulent combustion, we show that when the dimension is two and the flow of the ambient fluid is either weak or very strong, the level set of the effective burning velocity has flat pieces. Due to the lack of an applicable Hopf-type rigidity result, we need to identify the exact location of at least one flat piece. Implications on the effective flame front and other related inverse type problems are also discussed.
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