Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Strain induced slowdown of front propagation in random shear flow via analysis of G-equations


Author: Hongwei Gao
Journal: Proc. Amer. Math. Soc. 144 (2016), 3063-3076
MSC (2010): Primary 70H20; Secondary 76M50
DOI: https://doi.org/10.1090/proc/12930
Published electronically: November 20, 2015
MathSciNet review: 3487236
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that for the 2-dimensional case with random shear flow of the G-equation model with strain term, the strain term reduces the front propagation. Also an improvement of the main result by Armstrong-Souganidis is provided.


References [Enhancements On Off] (What's this?)

  • [1] Scott N. Armstrong and Panagiotis E. Souganidis, Stochastic homogenization of level-set convex Hamilton-Jacobi equations, Int. Math. Res. Not. IMRN 15 (2013), 3420-3449. MR 3089731
  • [2] S. N. Armstrong, H. V. Tran, and Y. Yu. Stochastic homogenization of nonconvex Hamilton-Jacobi equations in one space dimension, preprint, arXiv:1410.7053 [math.AP].
  • [3] P. Cardaliaguet, J. Nolen, and P. E. Souganidis, Homogenization and enhancement for the $ G$-equation, Arch. Ration. Mech. Anal. 199 (2011), no. 2, 527-561. MR 2763033 (2012k:35030), https://doi.org/10.1007/s00205-010-0332-8
  • [4] P. Clavin, P. Pelce, Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames, J. Fluid Mech. 124(1982), 219-237.
  • [5] Pierre Cardaliaguet and Panagiotis E. Souganidis, Homogenization and enhancement of the $ G$-equation in random environments, Comm. Pure Appl. Math. 66 (2013), no. 10, 1582-1628. MR 3084699, https://doi.org/10.1002/cpa.21449
  • [6] Lawrence C. Evans, Partial differential equations, 2nd ed., Graduate Studies in Mathematics, vol. 19, American Mathematical Society, Providence, RI, 2010. MR 2597943 (2011c:35002)
  • [7] H. Gao, Random homogenization of coercive Hamilton-Jacobi equations in 1d, preprint, arXiv:1507.07048 [math.AP]
  • [8] Pierre-Louis Lions and Panagiotis E. Souganidis, Correctors for the homogenization of Hamilton-Jacobi equations in the stationary ergodic setting, Comm. Pure Appl. Math. 56 (2003), no. 10, 1501-1524. MR 1988897 (2004m:35018), https://doi.org/10.1002/cpa.10101
  • [9] M. Matalon, B. J. Matkowsky, Flames as gasdynamic discontinuities, J. Fluid Mech. 124(1982), 239-259.
  • [10] James Nolen and Alexei Novikov, Homogenization of the G-equation with incompressible random drift in two dimensions, Commun. Math. Sci. 9 (2011), no. 2, 561-582. MR 2815685 (2012g:35025)
  • [11] Norbert Peters, Turbulent combustion, Cambridge Monographs on Mechanics, Cambridge University Press, Cambridge, 2000. MR 1792350 (2001j:80007)
  • [12] P. Ronney, Some open issues in premixed turbulent combustion, Modeling in Combustion Science (J. D. Buckmaster and T. Takeno, Eds.), Lecture Notes In Physics, Vol.449, Springer-Verlag, Berlin, 1-22, 1995.
  • [13] Jack Xin and Yifeng Yu, Periodic homogenization of the inviscid $ G$-equation for incompressible flows, Commun. Math. Sci. 8 (2010), no. 4, 1067-1078. MR 2744920 (2012d:76101)
  • [14] Jack Xin and Yifeng Yu, Front quenching in the G-equation model induced by straining of cellular flow, Arch. Ration. Mech. Anal. 214 (2014), no. 1, 1-34. MR 3237880, https://doi.org/10.1007/s00205-014-0751-z
  • [15] J. Xin and Y. Yu, Personal communication.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 70H20, 76M50

Retrieve articles in all journals with MSC (2010): 70H20, 76M50


Additional Information

Hongwei Gao
Affiliation: Department of Mathematics, University of California, Irvine, California 92697-3875
Email: hongweig@math.uci.edu

DOI: https://doi.org/10.1090/proc/12930
Keywords: Hamilton-Jacobi equation, level-set convex, stochastic homogenization, the G-equation, strain, random shear flow
Received by editor(s): November 16, 2014
Received by editor(s) in revised form: August 14, 2015
Published electronically: November 20, 2015
Additional Notes: The author was partially supported by DMS-1151919
Communicated by: Joachim Krieger
Article copyright: © Copyright 2015 American Mathematical Society

American Mathematical Society