2001/01/01 by A. Stevens, A F Stevens, George Papanicolaou +3 · 5 citations
Computer Science · Mathematics · Medicine · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #Mathematical and Theoretical Epidemiology and Ecology Models
paper · doi:10.1137/s0036139999361148
crossref issued 2001/01/01 · crossref published 2001/01/01 · crossref published-print 2001/01/01 · openalex publication_date 2001/01/01 · crossref created 2003/06/11 · crossref deposited 2020/03/21 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/31
An important problem in reactive flows is how to estimate the speed of front propagation, especially when inhomogeneities are present. Here we prove a variational characterization of the front speed for reaction-diffusion-advectionequations in periodically varying heterogeneous media. This formulation makes it possible to calculate sharp estimates for the speed explicitly. The method can be applied to any problem obeying a maximum principle. Three examples will be analyzed in detail: a shear flow problem, a problem with rapidly oscillating coefficients, and a discretized diffusion problem. In all cases the effects of the inhomogeneous medium on the speed are discussed in comparison to the homogeneous problem. For the shear flow problem, enhancement of the speed results.