Asymptotic estimates to quenching solutions of heat equations with weighted absorptions

作者：Wang, Wei; Zheng, Sining^*

来源：Asymptotic Analysis, 2010, 70(3-4): 125-139.

DOI：10.3233/ASY-2010-1006

• heat equations
• quenching time
• quenching set
• asymptotic estimates
• local energy estimates
• weighted absorptions

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.

• 出版日期2010
• 单位大连理工大学