Non-adiabatic KPP fronts with an arbitrary Lewis number
نویسندگان
چکیده
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 uniformly small. Finally, in the limit of large flow amplitudes A, we show that, depending on the flow structure, the infimum of the front speeds both may become 0 or grow linearly in A for A 1.
منابع مشابه
Travelling fronts for the thermodiffusive system with arbitrary Lewis numbers
We consider KPP-type systems in a cylinder with an arbitrary Lewis number (the ratio of thermal and material diffusivities) in the presence of a shear flow. We show that traveling fronts solutions exist for all Lewis numbers and approach uniform limits at the two ends of the cylinder.
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 کاملExistence and Non-existence of Fisher-KPP Transition Fronts
We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global in time solutions while creating a global in time bump-like solution. This is the first example of a medium in which no reaction-diffusion transition front exists. A weaker localized...
متن کاملQuenching and propagation in KPP reaction-diffusion equations with a heat loss
We consider a reaction-diffusion system of the KPP type in a shear flow and with a non-zero heat loss parameter. We establish criteria for the flame blow-off and propagation, and identify the propagation speed in terms of the exponential decay of the initial data. We prove existence of traveling fronts for all speeds c > max(0, c∗) in the case Le = 1, where c∗ ∈ R. That seems to be one of the f...
متن کاملAdmissible speeds of transition fronts for nonautonomous monostable equations
We consider a reaction-diffusion equation with a nonlinear term of the Fisher-KPP type, depending on time t and admitting two limits as t → ±∞. We derive the set of admissible asymptotic past and future speeds of transition fronts for such equation. We further show that any transition front which is non-critical as t → −∞ always admits two asymptotic past and future speeds. We finally describe ...
متن کامل