# Acceleration in integro-differential combustion equations

@inproceedings{Bouin2021AccelerationII, title={Acceleration in integro-differential combustion equations}, author={Emeric Bouin and J{\'e}r{\^o}me Coville and Guillaume Legendre}, year={2021} }

We study acceleration phenomena in monostable integro-differential equations with ignition nonlinearity. Our results cover fractional Laplace operators and standard convolutions in a unified way, which is also a contribution of this paper. To achieve this, we construct a sub-solution that captures the expected dynamics of the accelerating solution, and this is here the main difficulty. This study involves the flattening effect occurring in accelerated propagation phenomena.

## One Citation

Optimal Estimates on the Propagation of Reactions with Fractional Diffusion

- Mathematics
- 2021

We study the reaction-fractional-diffusion equation ut + (−∆)su = f(u) with ignition and monostable reactions f , and s ∈ (0, 1). We obtain the first optimal bounds on the propagation of front-like…

## References

SHOWING 1-10 OF 14 REFERENCES

Transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity

- Mathematics
- 2014

The present paper is devoted to the study of transition fronts in nonlocal reaction-diffusion equations with time heterogeneous nonlinearity of ignition type. It is proven that such an equation…

Regularity and stability of transition fronts in nonlocal equations with time heterogeneous ignition nonlinearity

- Mathematics
- 2015

The present paper is devoted to the investigation of various properties of transition fronts in nonlocal equations in heterogeneous media of ignition type, whose existence has been established by the…

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

- Mathematics
- 2007

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…

Propagation acceleration in reaction diffusion equations with anomalous diffusions

- Mathematics, Physics
- 2020

In this paper we consider the propagation speed in a reaction diffusion system with an anomalous Lévy process diffusion, modeled by a nonlocal equation with a fractional Laplacian and a generalized…

The Influence of Fractional Diffusion in Fisher-KPP Equations

- Mathematics
- 2013

We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast…

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…

Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations

- Mathematics
- 1997

The existence, uniqueness, and global exponential stability of traveling wave solutions of a class of nonlinear and nonlocal evolution equations are established. It is assumed that there are two…

Existence and asymptotics of fronts in non local combustion models

- Mathematics, Physics
- 2011

We prove the existence and provide the asymptotics for non local fronts in homogeneous media.

Potential Analysis of Stable Processes and its Extensions

- Mathematics
- 2009

Boundary Potential Theory for Schr#x00F6 dinger Operators Based on Fractional Laplacian.- Nontangential Convergence for #x03B1 -harmonic Functions.- Eigenvalues and Eigenfunctions for Stable…

Asymptotic behavior for nonlocal diffusion equations

- Mathematics
- 2006

We study the asymptotic behavior for nonlocal diffusion models of the form ut=J∗u−u in the whole RN or in a bounded smooth domain with Dirichlet or Neumann boundary conditions. In RN we obtain that…