Title: Propagation in reaction-diffusion equations with non-local diffusion

Abstract: We discuss the propagation of solutions of multidimensional reaction-diffusion equations u_t = Hu + f(u) with homogeneous media and non-local diffusion (Hu = J*u - u). Such a PDE and its variations are widely used in modeling a host of natural processes, including combustion, population dynamics and diffusion under chemical reaction. The case of classical diffusion (i.e., Laplacian in place of H) was investigated by Aronson and Weinberger (1978), who showed the existence of asymptotic spreading speed c_f for a large class of reaction functions f. Namely, in the prototypical situation, the solution of the PDE will spread across the space with speed c_f. In the talk, I will show how to extend this result to the case of non-local diffusion.