Large scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales. (English) Zbl 0839.76093

Majda, Andrew J.; Souganidis, Panagiotis E.

Nonlinearity 7, No. 1, 1-30 (1994).

Simplified effective equations for the large scale front propagation of turbulent reaction-diffusion equations are developed in the simplest prototypical situation involving advection by turbulent velocity fields with two separated scales. A rigorous theory for large scale front propagation is developed, utilizing PDE techniques for viscosity solutions together with homogenization theory for Hamilton-Jacobi equations. The subtle issues regarding the validity of a Huygens principle for the effective large scale front propagation as well as elementary upper and lower bounds on the propagating front are developed. Simple examples involving small scale periodic shear layers are also presented.

MSC:

76V05	Reaction effects in flows
35K57	Reaction-diffusion equations

Keywords:

PDE techniques; viscosity solutions; homogenization theory for Hamilton-Jacobi equations; Huygens principle; upper and lower bounds; small scale periodic shear layers