☆ 4.5 Article

Inverse problems, non-roundness and flat pieces of the effective burning velocity from an inviscid quadratic Hamilton-Jacobi model

NONLINEARITY (2017)

Journal

NONLINEARITY

Volume 30, Issue 5, Pages 1853-1875

Publisher

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

Mathematics, Applied Physics, Mathematical

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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Abstract

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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