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December 2010 Periodic homogenization of the inviscid G-equation for incompressible flows
Jack Xin, Yifeng Yu
Commun. Math. Sci. 8(4): 1067-1078 (December 2010).


G-equations are popular front propagation models in combustion literature and describe the front motion law of normal velocity equal to a constant plus the normal projection of fluid velocity. G-equations are Hamilton-Jacobi equations with convex but non-coercive Hamiltonians. We prove homogenization of the inviscid G-equation for space periodic incompressible flows. This extends a two space dimensional result in "Periodic homogenization of G-equations and viscosity effects," Nonlinearity, to appear. We construct approximate correctors to bypass the lack of compactness due to the non-coercive Hamiltonian. The existence of approximate correctors rely on a local reachability property of the controlled flow trajectory as well as incompressibility of the flow. Homogenization then follows from the comparison principle and the perturbed test function method. The effective Hamiltonian is convex and homogeneous of degree one. It is also coercive if we further assume that the flow is mean zero.


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Jack Xin. Yifeng Yu. "Periodic homogenization of the inviscid G-equation for incompressible flows." Commun. Math. Sci. 8 (4) 1067 - 1078, December 2010.


Published: December 2010
First available in Project Euclid: 2 November 2010

zbMATH: 1372.76085
MathSciNet: MR2744920

Primary: 70H20 , 76M45 , 76M50 , 76N20

Keywords: controlled flow , incompressibility , local reachability , Non-coercive Hamilton-Jacobi equations , Periodic homogenization

Rights: Copyright © 2010 International Press of Boston

Vol.8 • No. 4 • December 2010
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