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Indexed by:期刊论文

Date of Publication:2010-01-01

Journal:ASYMPTOTIC ANALYSIS

Included Journals:SCIE、EI、Scopus

Volume:70

Issue:3-4

Page Number:125-139

ISSN No.:0921-7134

Key Words:heat equations; quenching time; quenching set; asymptotic estimates; local energy estimates; weighted absorptions

Abstract: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.