Exponential propagation for fractional reaction-diffusion cooperative systems with fast decaying initial conditions

TL;DR

This paper investigates the exponential speed of solution propagation in fractional reaction-diffusion cooperative systems, revealing the precise exponent based on fractional Laplacians and eigenvalues, independent of spatial direction.

Contribution

It provides the first detailed analysis of exponential propagation speed in fractional reaction-diffusion systems with explicit dependence on fractional Laplacian indices and eigenvalues.

Findings

Propagation speed is exponential in time.

The exact exponent depends on fractional Laplacian indices and principal eigenvalue.

Speed is isotropic, not depending on space direction.

Abstract

We study the time asymptotic propagation of solutions to the reaction-diffusion cooperative systems with fractional diffusion. We prove that the propagation speed is exponential in time, and we find the precise exponent of propagation. This exponent depends on the smallest index of the fractional laplacians and on the principal eigenvalue of the matrix DF(0) where F is the reaction term. We also note that this speed does not depend on the space direction.