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

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Díaz Díaz, Jesús Ildefonso (2012) A note on spatial uniformation for Fisher-KPP type equations with a concentration dependent diffusion. International Journal of Dynamical Systems and Differential Equations, 4 (1-2). pp. 70-77. ISSN 1752-3583

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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.


Item Type:Article
Uncontrolled Keywords:Gradient estimates; quasilinear Fisher-KPP type equations; regularising effects; spatial uniformation.
Subjects:Sciences > Mathematics > Differential equations
ID Code:29667
Deposited On:23 Apr 2015 06:36
Last Modified:12 Dec 2018 15:07

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