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论文类型：期刊论文

发表时间：2010-01-01

发表刊物：ASYMPTOTIC ANALYSIS

收录刊物：SCIE、EI、Scopus

卷号：70

期号：3-4

页面范围：125-139

ISSN号：0921-7134

关键字：heat equations; quenching time; quenching set; asymptotic estimates; local energy estimates; weighted absorptions

摘要：This paper studies heat equations with weighted nonlinear absorptions of the form u(t) = u(xx) - Mf(x)u(-p) in (-1, 1) x(0, T) subject to Dirichlet boundary conditions u(-1, t) = u(1, t) = 1 and initial data phi(x). The asymptotic estimates to quenching time and set of solutions as M -> +infinity is established by local energy estimates. It is obtained that the quenching time T similar to m/p+1 . M(-1) with m = 1/max(x)(f(x)/phi(p+1)(x)) as M -> +infinity. It is shown also how the quenching set concentrates near the maximum points of f/phi(p+1) for large M.