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.

DOI: 10.1504/IJDSDE.2012.045995

International Journal of Dynamical Systems and Differential Equations, 2012 Vol.4 No.1/2, pp.70 - 77

Available online: 19 Mar 2012 *

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