Fast propagation for fractional KPP equations with slowly decaying initial conditions

Abstract:

In this paper we study the large-time behavior of solutions of one-dimensional fractional Fisher-KPP reaction-diffusion equations, when the initial condition is asymptotically frontlike and it decays at infinity more slowly than a power x?b, where b < 2? and ? ? (0, 1) is the order of the fractional Laplacian. We prove that the level sets of the solutions move exponentially fast as time goes to infinity. Moreover, a quantitative estimate of motion of the level sets is obtained in terms of the decay of the initial condition. © 2013 Society for Industrial and Applied Mathematics.

Año de publicación:

2013

Keywords:

• KPP
• Fractional reaction-diffusion
• Aasymptotic behavior

Fuente:

scopus