Boundary layers and KPP fronts in a cellular flow
نویسندگان
چکیده
We study an eigenvalue problem associated with a reaction-diffusionadvection equation of the KPP type in a cellular flow. We obtain upper and lower bounds on the eigenvalues in the regime of a large flow amplitude A 1. It follows that the minimal pulsating traveling front speed c∗(A) satisfies the upper and lower bounds C1A ≤ c∗(A) ≤ C2A. Physically, the speed enhancement is related to the boundary layer structure of the associated eigenfunction – accordingly, we establish an “averaging along the streamlines” principle for the unique positive eigenfunction.
منابع مشابه
Finite Element Computation of KPP Front Speeds in Cellular and Cat's Eye Flows
We compute the front speeds of the Kolmogorov-Petrovsky-Piskunov (KPP) reactive fronts in two prototypes of periodic incompressible flows (the cellular flows and the cat’s eye flows). The computation is based on adaptive streamline diffusion methods for the advection-diffusion type principal eigenvalue problem associated with the KPP front speeds. In the large amplitude regime, internal layers ...
متن کاملNon-adiabatic KPP fronts with an arbitrary Lewis number
We establish existence of travelling fronts in thermo-diffusive systems of the KPP type in a shear flow with an arbitrary Lewis number and a positive heat-loss at the boundary. We then prove that the leftover concentration behind the front is positive, and that it is small when the heat-loss is small. On the other hand, when the heat-loss approaches a critical value, the temperature becomes uni...
متن کاملBounds on the speed of propagation of the KPP fronts in a cellular flow
We consider a reaction-diffusion-advection equation with a nonlinearity of the KPP type in a cellular flow. We show that the minimal pulsating traveling front speed c∗(A) in a flow of amplitude A satisfies the upper and lower bounds C1A ≤ c∗(A) ≤ C2A for A 1. We also analyze a related eigenvalue problem and establish an “averaging along the streamlines” principle for the positive eigenfunction ...
متن کاملExistence of Kpp Type Fronts in Space-time Periodic Shear Flows and a Study of Minimal Speeds Based on Variational Principle
We prove the existence of reaction-diffusion traveling fronts in mean zero space-time periodic shear flows for nonnegative reactions including the classical KPP (Kolmogorov-Petrovsky-Piskunov) nonlinearity. For the KPP nonlinearity, the minimal front speed is characterized by a variational principle involving the principal eigenvalue of a space-time periodic parabolic operator. Analysis of the ...
متن کاملTransition Fronts in Inhomogeneous Fisher-kpp Reaction-diffusion Equations
We use a new method in the study of Fisher-KPP reaction-diffusion equations to prove existence of transition fronts for inhomogeneous KPP-type non-linearities in one spatial dimension. We also obtain new estimates on entire solutions of some KPP reactiondiffusion equations in several spatial dimensions. Our method is based on the construction of suband super-solutions to the non-linear PDE from...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005