Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2010-01-01

Journal: ASYMPTOTIC ANALYSIS

Included Journals: Scopus、EI、SCIE

Volume: 70

Issue: 3-4

Page Number: 125-139

ISSN: 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.