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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
59/1999

Variational principles for propagation speeds in inhomogeneous media

Steffen Heinze, George Papanicolaou and Angela Stevens

Abstract

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.

Received:
Sep 23, 1999
Published:
Sep 23, 1999

Related publications

inJournal
2001 Repository Open Access
Steffen Heinze, George Papanicolaou and Angela Stevens

Variational principles for propagation speeds in inhomogeneous media

In: SIAM journal on applied mathematics, 62 (2001) 1, 129-148 (electronic)