%0 Journal Article
%A Díaz Díaz, Jesús Ildefonso
%T Pointwise gradient estimates and stabilization for Fisher-KPP type equations with a concentration dependent diffusion
%D 2010
%@ 1752-3583
%U https://hdl.handle.net/20.500.14352/44520
%X We prove a pointwise gradient estimate for the bounded weak solution of the Cauchy problem associated to the quasilinear Fisher-KPP type equation ut ='(u)xx + (u) when ' satisÖes that '(0)=0; and (u) is vanishing only for levels u = 0 and u = 1. As a Örst consequence we prove that the bounded weak solution becomes instantaneously a continuous function even if the initial datum is merely a discontinuous bounded function. Moreover the obtained estimates also prove the stabilization of the gradient of bounded weak solutions as t ! +1 for suitable initial data.
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