TY - JOUR
T1 - Brownian fluctuations of flame fronts with small random advection
AU - Henderson, Christopher
AU - Souganidis, Panagiotis E.
N1 - Funding Information:
Henderson was partially supported by National Science Foundation Research Training Grant DMS-1246999 and Grant DMS-2003110. Souganidis was partially supported by the National Science Foundation Grants DMS-1266383 and DMS-1600129 and the Office for Naval Research Grant N00014-17-1-2095.
Publisher Copyright:
© 2020 World Scientific Publishing Company.
PY - 2020/6/30
Y1 - 2020/6/30
N2 - We study the effect of small random advection in two models in turbulent combustion. Assuming that the velocity field decorrelates sufficiently fast, we (i) identify the order of the fluctuations of the front with respect to the size of the advection; and (ii) characterize them by the solution of a Hamilton-Jacobi equation forced by white noise. In the simplest case, the result yields, for both models, a front with Brownian fluctuations of the same scale as the size of the advection. That the fluctuations are the same for both models is somewhat surprising, in view of known differences between the two models.
AB - We study the effect of small random advection in two models in turbulent combustion. Assuming that the velocity field decorrelates sufficiently fast, we (i) identify the order of the fluctuations of the front with respect to the size of the advection; and (ii) characterize them by the solution of a Hamilton-Jacobi equation forced by white noise. In the simplest case, the result yields, for both models, a front with Brownian fluctuations of the same scale as the size of the advection. That the fluctuations are the same for both models is somewhat surprising, in view of known differences between the two models.
KW - Fisher-KPP equation
KW - Front propagation
KW - G-equation
KW - Hamilton-Jacobi equations
KW - stochastic advection
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U2 - 10.1142/S0218202520500256
DO - 10.1142/S0218202520500256
M3 - Article
AN - SCOPUS:85090710978
VL - 30
SP - 1375
EP - 1406
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
SN - 0218-2025
IS - 7
ER -