Skip to main content

Reaction-diffusion front speeds in spatially-temporally periodic shear flows

Publication ,  Journal Article
Nolen, J; Xin, J
Published in: Multiscale Modeling and Simulation
January 1, 2003

We study the asymptotics of two space dimensional reaction-diffusion front speeds through mean zero space-time periodic shears using both analytical and numerical methods. The analysis hinges on traveling fronts and their estimates based on qualitative properties such as monotonicity and a priori integral inequalities. The computation uses an explicit second order upwind finite difference method to provide more quantitative information. At small shear amplitudes, front speeds are enhanced by an amount proportional to shear amplitude squared. The proportionality constant has a closed form expression. It decreases with increasing shear temporal frequency and is independent of the form of the known reaction nonlinearities. At large shear amplitudes and for all reaction nonlinearities, the enhanced speeds grow proportional to shear amplitude and are again decreasing with increasing shear temporal frequencies. The results extend previous ones in the literature on front speeds through spatially periodic shears and show front speed slowdown due to shear direction switching in time.

Duke Scholars

Published In

Multiscale Modeling and Simulation

DOI

EISSN

1540-3467

ISSN

1540-3459

Publication Date

January 1, 2003

Volume

1

Issue

4

Start / End Page

554 / 570

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Nolen, J., & Xin, J. (2003). Reaction-diffusion front speeds in spatially-temporally periodic shear flows. Multiscale Modeling and Simulation, 1(4), 554–570. https://doi.org/10.1137/S1540345902420234
Nolen, J., and J. Xin. “Reaction-diffusion front speeds in spatially-temporally periodic shear flows.” Multiscale Modeling and Simulation 1, no. 4 (January 1, 2003): 554–70. https://doi.org/10.1137/S1540345902420234.
Nolen J, Xin J. Reaction-diffusion front speeds in spatially-temporally periodic shear flows. Multiscale Modeling and Simulation. 2003 Jan 1;1(4):554–70.
Nolen, J., and J. Xin. “Reaction-diffusion front speeds in spatially-temporally periodic shear flows.” Multiscale Modeling and Simulation, vol. 1, no. 4, Jan. 2003, pp. 554–70. Scopus, doi:10.1137/S1540345902420234.
Nolen J, Xin J. Reaction-diffusion front speeds in spatially-temporally periodic shear flows. Multiscale Modeling and Simulation. 2003 Jan 1;1(4):554–570.

Published In

Multiscale Modeling and Simulation

DOI

EISSN

1540-3467

ISSN

1540-3459

Publication Date

January 1, 2003

Volume

1

Issue

4

Start / End Page

554 / 570

Related Subject Headings

  • Applied Mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics