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Archive for Rational Mechanics and Analysis

, Volume 154, Issue 1, pp 53–91 | Cite as

Bulk Burning Rate in¶Passive–Reactive Diffusion

  • Peter Constantin
  • Alexander Kiselev
  • Adam Oberman
  • Leonid Ryzhik
Article

Abstract

We consider a passive scalar that is advected by a prescribed mean zero divergence-free velocity field, diffuses, and reacts according to a KPP-type nonlinear reaction. We introduce a quantity, the bulk burning rate, that makes both mathematical and physical sense in general situations and extends the often ill-defined notion of front speed. We establish rigorous lower bounds for the bulk burning rate that are linear in the amplitude of the advecting velocity for a large class of flows. These “percolating” flows are characterized by the presence of tubes of streamlines connecting distant regions of burned and unburned material and generalize shear flows. The bound contains geometric information on the velocity streamlines and degenerates when these oscillate on scales that are finer than the width of the laminar burning region. We give also examples of very different kind of flows, cellular flows with closed streamlines, and rigorously prove that these can produce only sub-linea enhancement of the bulk burning rate.

Keywords

Burning Rate Percolate Travel Wave Solution Reactive Diffusion Advecting Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Peter Constantin
    • 1
  • Alexander Kiselev
    • 1
  • Adam Oberman
    • 1
  • Leonid Ryzhik
    • 1
  1. 1.Department of Mathematics¶University of Chicago¶Chicago IL 60637USA

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