Enhancement of the traveling front speeds in reaction-diffusion equations with advection

Journal Article (Journal Article)

We establish rigorous lower bounds on the speed of traveling fronts and on the bulk burning rate in reaction-diffusion equation with passive advection. The non-linearity is assumed to be of either KPP or ignition type. We consider two main classes of flows. Percolating flows, which are characterized by the presence of long tubes of streamlines mixing hot and cold material, lead to strong speed-up of burning which is linear in the amplitude of the flow, U. On the other hand the cellular flows, which have closed streamlines, are shown to produce weaker increase in reaction. For such flows we get a lower bound which grows as U1/5 for a large amplitude of the flow. © 2001 Éditions scientifiques et médicales Elsevier SAS.

Full Text

Duke Authors

Cited Authors

  • Kiselev, A; Ryzhik, L

Published Date

  • January 1, 2001

Published In

Volume / Issue

  • 18 / 3

Start / End Page

  • 309 - 358

International Standard Serial Number (ISSN)

  • 0294-1449

Digital Object Identifier (DOI)

  • 10.1016/S0294-1449(01)00068-3

Citation Source

  • Scopus