A note on spatial uniformation for Fisher-KPP type equations with a concentration dependent diffusion
by J.I. Díaz
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 4, No. 1/2, 2012

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.

Online publication date: Wed, 10-Dec-2014

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