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Approaching an extinction point in one-dimensional semilinear heat-equations with strong absorption

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Herrero, Miguel A. and Velázquez, J.J. L. (1992) Approaching an extinction point in one-dimensional semilinear heat-equations with strong absorption. Journal of Mathematical Analysis and Applications, 170 (2). pp. 353-381. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/0022247X92900248


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Abstract

This paper deals with the Cauchy problem
u(t)-u(xx)+u(p)=0; -infinity<x<+infinity, t>o,
u(x, 0)=u(0)(x); -infinity<x<+infinity,
where 0<p<1 and u(0)(X)is continuous, nonnegative, and bounded. In this case, solutions are known to vanish in a finite time T, and interfaces separating the regions where u(x,t)>0 and u(x,t)=0 appear when t is close to T. We describe here all possible asymptotic behaviours of solutions and interfaces near an extinction point as the extinction time is approached. We also give conditions under which some of these behaviours actually occur.


Item Type:Article
Uncontrolled Keywords:One-dimensional semilinear heat equations; interfaces; extinction point
Subjects:Sciences > Mathematics > Differential equations
ID Code:17346
Deposited On:10 Dec 2012 09:07
Last Modified:12 Dec 2018 15:08

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