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

Wenjia Jing Tsinghua University Hung V. Tran University of Wisconsin at Madison Yifeng Yu University of California at Irvine

Dynamical Systems mathscidoc:1703.11003

Nonlinearity, 2017
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. Motivated by results of Bangert and applications in turbulent combus- tion, 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.
Aubry-Mather theory, magnetic Hamiltonian, rigidity, effective burning rate, turbulent combustion
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  • paper accepted, to appear
@inproceedings{wenjia2017inverse,
  title={INVERSE PROBLEMS, NON-ROUNDNESS AND FLAT PIECES OF THE EFFECTIVE BURNING VELOCITY FROM AN INVISCID QUADRATIC HAMILTON-JACOBI MODEL},
  author={Wenjia Jing, Hung V. Tran, and Yifeng Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170315071237717195712},
  booktitle={Nonlinearity},
  year={2017},
}
Wenjia Jing, Hung V. Tran, and Yifeng Yu. INVERSE PROBLEMS, NON-ROUNDNESS AND FLAT PIECES OF THE EFFECTIVE BURNING VELOCITY FROM AN INVISCID QUADRATIC HAMILTON-JACOBI MODEL. 2017. In Nonlinearity. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170315071237717195712.
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