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A note on spatial uniformation for Fisher-KPP type equations with a concentration dependent diffusion

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2012
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Inderscience publishers
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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.
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