Title: A note on spatial uniformation for Fisher-KPP type equations with a concentration dependent diffusion
Authors: J.I. Díaz
Addresses: Univ. Complutense de Madrid, Fac. de Matemáticas, Madrid, 28040, Spain
Abstract: We prove a pointwise gradient estimate for the solution of the Cauchy problem associated to the quasilinear Fisher-KPP type equation with a diffusion coefficient φ(u) satisfying that φ(0) = 0, φ(1) = 1 and a source term ψ(u) which is vanishing only for levels u = 0 and u = 1. As consequence we prove that the bounded weak solution becomes instantaneously a continuous function even if the initial datum is merely a bounded function.
Keywords: gradient estimates; quasilinear Fisher-KPP type equations; regularising effects; spatial uniformation; concentration dependent diffusion.
International Journal of Dynamical Systems and Differential Equations, 2012 Vol.4 No.1/2, pp.70 - 77
Available online: 19 Mar 2012 *Full-text access for editors Access for subscribers Purchase this article Comment on this article