Title: Pointwise gradient estimates and stabilization for Fisher-KPP type equations with a concentration dependent diffusion
Abstract: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 ' satisOes that '(0)=0; and (u) ...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 ' satisOes that '(0)=0; and (u) is vanishing only for levels u = 0 and u = 1. As a Orst 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.Read More
Publication Year: 2010
Publication Date: 2010-01-01
Language: en
Type: article
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Cited By Count: 1
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