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Variational principles for propagation speeds in inhomogeneous media
Steffen Heinze, George Papanicolaou and Angela Stevens
We consider a scalar reaction-diffusion equation with bistable nonlinearity in a medium with spatially varying diffusion and drift coefficients. A major problem in reactive flows is the derivation of upper and lower bounds for the effective speed of propagation. Using a min/max characterization of the traveling wave velocity we will provide such estimates for shear flows, equations near the homogenization limit and a spatially discretized problem. The method presented here can be applied to any other problem possessing a maximum principle.