Propagation acceleration in reaction diffusion equations with anomalous
diffusions
Propagation acceleration in reaction diffusion equations with anomalous
diffusions
In this paper, we are interested in the properties of solution of the nonlocal equation $$\begin{cases}u_t+(-\Delta)^su=f(u),\quad t>0, \ x\in\mathbb{R}\\ u(0,x)=u_0(x),\quad x\in\mathbb{R}\end{cases}$$ where $0\le u_0<1$ is a Heaviside type function, $\Delta^s$ stands for the fractional Laplacian with $s\in (0,1)$, and $f\in C([0,1],\mathbb{R}^+)$ is a non negative nonlinearity such that $f(0)=f(1)=0$ and …