Power-like delay in time inhomogeneous Fisher-KPP equations
نویسندگان
چکیده
We consider solutions of the KPP equation with a time-dependent diffusivity of the form σ(t/T ). For an initial condition that is compactly supported, we show that when σ(s) is increasing in time the front position at time T is X(T ) = c∗T − ν̄T +O(log T ). That is, X(T ) lags behind the linear front by an amount that is algebraic in T , not by the Bramson correction (3/2) log T as in the uniform medium. This refines a result by Fang and Zeitouni.
منابع مشابه
Existence 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 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 کاملRemark on Stability of Traveling Waves for Nonlocal Fisher-kpp Equations
t − n 2 . These convergent rates are optimal in the sense with L-initial perturbation. The adopted approach is the weighted energy method combining Fourier transform. It is also realized that, the effect of time-delay essentially causes the decay rate of the solution slowly down. These results significantly generalize and develop the existing study [37] for 1-D time-delayed Fisher-KPP type reac...
متن کاملGlobal Stability of Planar Traveling Waves For Nonlocal Fisher-KPP Type Reaction-Diffusion Equations in Multi-Dimensional Space
This paper is concerned with a class of nonlocal Fisher-KPP type reaction-diffusion equations in n-dimensional space with or without time-delay. It is proved that, all noncritical planar wavefronts are globally stable in the form of t− n 2 e−μt for some constant μ > 0, where the value of μ depends on the size of the time-delay, and the critical planar wavefronts are globally stable in the algeb...
متن کاملA short proof of the logarithmic Bramson correction in Fisher-KPP equations
In this paper, we explain in simple PDE terms a famous result of Bramson about the logarithmic delay of the position of the solutions u(t, x) of Fisher-KPP reaction-diffusion equations in R, with respect to the position of the travelling front with minimal speed. Our proof is based on the comparison of u to the solutions of linearized equations with Dirichlet boundary conditions at the position...
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 2013