The Freidlin-Gartner formula for general reaction terms

How does the spreading speed associated with the Fisher-KPP equation depend on random stationary diffusion and reaction terms?

We consider one-dimensional reaction-diffusion equations of Fisher-KPP type with random stationary ergodic coefficients. A classical result of Freidlin and Gartner [16] yields that the solutions of the initial value problems associated with compactly supported initial data admit a linear spreading speed almost surely. We use in this paper a new characterization of this spreading speed recently proved in [8] in order to investigate the dependence of this speed with respect to the heterogeneity of the diffusion and reaction terms. We prove in particular that adding a reaction term with null aver…

周期性介质中的反应扩散方程：向脉动前沿收敛

Reaction-diffusion equations in periodic media: convergence to pulsating fronts

研究周期性介质中反应扩散-对流方程的长期行为，证明在弱稳定性和脉动前沿存在性假设下，解的长期动力学中前沿轮廓出现，无论初始支持有界还是无界，并探讨了入侵解的渐近入侵形状和几何性质。

Spreading sets and one-dimensional symmetry for reaction-diffusion equations

We consider reaction-diffusion equations $\partial_tu=Δu+f(u)$ in the whole space $\mathbb{R}^N$ and we are interested in the large-time dynamics of solutions ranging in the interval $[0,1]$, with general unbounded initial support. Under the hypothesis of the existence of a traveling front connecting $0$ and $1$ with a positive speed, we discuss the existence of spreading speeds and spreading sets, which describe the large-time global shape of the level sets of the solutions. The spreading speed in any direction is expressed as a Freidlin-Gärtner type formula. This formula holds under general …

R^n 上由超线性乘性噪声驱动的分数阶反应-扩散方程的一致大偏差原理

Uniform Large Deviation Principles of Fractional Reaction-Diffusion Equations Driven by Superlinear Multiplicative Noise on R^n

本文利用弱收敛方法，并借助漂移耗散性与解的一致尾端估计，证明了 R^n 上含超线性乘性噪声的分数阶随机反应-扩散方程在噪声趋零时的两类一致大偏差原理。

R^n上由乘性噪声驱动的分数阶反应扩散方程不变测度的大偏差

Large Deviations of Invariant Measures of Fractional Reaction-Diffusion Equations Driven by Multiplicative Noise on R^n

本文针对R^n上带多项式反应项、由无界乘性噪声驱动的分数阶随机反应扩散方程，建立其不变测度的大偏差，为该类无界域方程不变测度大偏差的首个相关结果。