Math @ Duke

Publications [#287356] of James H. Nolen
Papers Published
 Nolen, J; Novikov, A, Homogenization of the Gequation with incompressible random drift in two dimensions,
Communications in Mathematical Sciences, vol. 9 no. 2
(2011),
pp. 561582, ISSN 15396746 [pdf]
(last updated on 2018/06/24)
Abstract: We study the homogenization limit of solutions to the Gequation with random drift. This HamiltonJacobi equation is a model for flame propagation in a turbulent fluid in the regime of thin flames. For a fluid velocity field that is statistically stationary and ergodic, we prove sufficient conditions for homogenization to hold with probability one. These conditions are expressed in terms of travel times for the associated control problem. When the spatial dimension is equal to two and the fluid velocity is divergencefree, we verify that these conditions hold under suitable assumptions about the growth of the random stream function. © 2011 International Press.


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