Enhancement of the traveling front speeds in reaction-diffusion equations with advection
Publication
, Journal Article
Kiselev, A; Ryzhik, L
Published in: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
January 1, 2001
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.
Duke Scholars
Published In
Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
DOI
ISSN
0294-1449
Publication Date
January 1, 2001
Volume
18
Issue
3
Start / End Page
309 / 358
Related Subject Headings
- General Mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Kiselev, A., & Ryzhik, L. (2001). Enhancement of the traveling front speeds in reaction-diffusion equations with advection. Annales de l’Institut Henri Poincare (C) Analyse Non Lineaire, 18(3), 309–358. https://doi.org/10.1016/S0294-1449(01)00068-3
Kiselev, A., and L. Ryzhik. “Enhancement of the traveling front speeds in reaction-diffusion equations with advection.” Annales de l’Institut Henri Poincare (C) Analyse Non Lineaire 18, no. 3 (January 1, 2001): 309–58. https://doi.org/10.1016/S0294-1449(01)00068-3.
Kiselev A, Ryzhik L. Enhancement of the traveling front speeds in reaction-diffusion equations with advection. Annales de l’Institut Henri Poincare (C) Analyse Non Lineaire. 2001 Jan 1;18(3):309–58.
Kiselev, A., and L. Ryzhik. “Enhancement of the traveling front speeds in reaction-diffusion equations with advection.” Annales de l’Institut Henri Poincare (C) Analyse Non Lineaire, vol. 18, no. 3, Jan. 2001, pp. 309–58. Scopus, doi:10.1016/S0294-1449(01)00068-3.
Kiselev A, Ryzhik L. Enhancement of the traveling front speeds in reaction-diffusion equations with advection. Annales de l’Institut Henri Poincare (C) Analyse Non Lineaire. 2001 Jan 1;18(3):309–358.
Published In
Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
DOI
ISSN
0294-1449
Publication Date
January 1, 2001
Volume
18
Issue
3
Start / End Page
309 / 358
Related Subject Headings
- General Mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics