• Corpus ID: 245704536

# Quantifying the threshold phenomena for propagation in nonlocal diffusion equations

@inproceedings{Alfaro2022QuantifyingTT,
title={Quantifying the threshold phenomena for propagation in nonlocal diffusion equations},
author={Matthieu Alfaro and Arnaud Ducrot and Hao Kang},
year={2022}
}
• Published 5 January 2022
• Mathematics
We are interested in the threshold phenomena for propagation in nonlocal diffusion equations with some compactly supported initial data. In the so-called bistable and ignition cases, we provide the first quantitative estimates for such phenomena. The outcomes dramatically depend on the tails of the dispersal kernel and can take a large variety of different forms. The strategy is to combine sharp estimates of the tails of the sum of i.i.d. random variables (coming, in particular, from large…
1 Citations

## Tables from this paper

### Large deviations and the emergence of a logarithmic delay in a nonlocal Fisher-KPP equation

We study a variant of the Fisher-KPP equation with nonlocal dispersal. Using the theory of large deviations, we show the emergence of a “Bramson-like” logarithmic delay for the linearised equation

## References

SHOWING 1-10 OF 32 REFERENCES

### Quantitative Estimates of the Threshold Phenomena for Propagation in Reaction-Diffusion Equations

• Mathematics
SIAM J. Appl. Dyn. Syst.
• 2020
In the so-called ignition and bistable cases, the first sharp quantitative estimate on the (sharp) threshold values is proved and numerical explorations allow to conjecture some refined estimates.

### Threshold phenomena for symmetric decreasing solutions of reaction-diffusion equations

• Mathematics
• 2013
We study the long time behavior of solutions of the Cauchy problem for nonlinear reaction-diffusion equations in one space dimension with the nonlinearity of bistable, ignition or monostable type. We

### On a non-local equation arising in population dynamics

• Mathematics
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
• 2007
We study a one-dimensional non-local variant of Fisher's equation describing the spatial spread of a mutant in a given population, and its generalization to the so-called monostable nonlinearity. The

### A non-local bistable reaction-diffusion equation with a gap

• Mathematics
• 2016
Non-local reaction-diffusion equations arise naturally to account for diffusions involving jumps rather than local diffusions related to Brownian motion. In ecology, long distance dispersal require

### Traveling Waves in a Convolution Model for Phase Transitions

• Mathematics
• 1997
The existence, uniqueness, stability and regularity properties of traveling-wave solutions of a bistable nonlinear integrodifferential equation are established, as well as their global asymptotic

### Threshold phenomena for symmetric-decreasing radial solutions of reaction-diffusion equations

• Mathematics
• 2016
We study the long time behavior of positive solutions of the Cauchy problem for nonlinear reaction-diffusion equations in \begin{document}$\mathbb{R}^N$\end{document} with bistable, ignition or

### Travelling fronts in asymmetric nonlocal reaction diffusion equations: The bistable and ignition cases

This paper is devoted to the study of the travelling front solutions which appear in a nonlocal reaction-diffusion equations of the form $$\frac{\partial u}{\partial t}=\j\star u -u +f(u).$$ When the

### Traveling wave solutions to some reaction diffusion equations with fractional Laplacians

• Mathematics
• 2015
We show the nonexistence of traveling wave solutions in the combustion model with fractional Laplacian $$\displaystyle (-\Delta )^s$$(-Δ)s when $$\displaystyle s\in (0,1/2]$$s∈(0,1/2]. Our method can

### Convergence and sharp thresholds for propagation in nonlinear diffusion problems

• Mathematics
• 2010
We study the Cauchy problem utDuxxCf.u/ .t > 0; x2 R 1 /; u.0;x/Du0.x/ .x2 R 1 /; wheref.u/ is a locally Lipschitz continuous function satisfyingf.0/D 0. We show that any non- negative bounded