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Pointwise gradient estimates and stabilization for Fisher-KPP type equations with a concentration dependent diffusion

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Díaz Díaz, Jesús Ildefonso (2010) Pointwise gradient estimates and stabilization for Fisher-KPP type equations with a concentration dependent diffusion. International Journal of Dynamical Systems and Differential Equations . ISSN 1752-3583

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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 ' 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.


Item Type:Article
Subjects:Sciences > Mathematics > Differential equations
ID Code:29736
Deposited On:27 Apr 2015 10:25
Last Modified:12 Dec 2018 15:07

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