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Asymptotic properties of a semilinear heat equation with strong absorption and small diffusion

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Herrero, Miguel A. and Velázquez, J.J. L. (1990) Asymptotic properties of a semilinear heat equation with strong absorption and small diffusion. Mathematische Annalen, 288 (4). pp. 675-695. ISSN 0025-5831

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Abstract

In this paper the authors study the asymptotic behaviour of solutions uε(x,t) of the Cauchy problems as ε goes to zero: ut−εΔu+up=0, x∈RN, t>0; u(x,0)=u0(x), x∈RN, 0<p<1. Compared with the explicit solution u¯(x,t) and the extinction time T0E(x) of the corresponding spatially independent initial value problem: ut+up=0, x∈RN, t>0; u(x,0)=u0(x), x∈RN, it is proved under certain assumptions that uε(x,t)→u¯(x,t) as ε↓0 uniformly on compact subsets of RN ×[0,∞) and, moreover, a precise estimate is given. Local and global estimates for extinction time are also given. The proofs are somewhat technical


Item Type:Article
Uncontrolled Keywords:Blow-up time; parabolic equations; variational inequalities; thermal waves; support; semilinear heat equation; strong absorption; small diffusion; Cauchy problems; convergence; extinction times
Subjects:Sciences > Mathematics > Differential equations
ID Code:18093
Deposited On:31 Jan 2013 09:10
Last Modified:12 Dec 2018 15:08

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