Blow-Up Solutions for Quasilinear Heat Equations with Nonlinear Boundary Conditions

摘要：

In this paper, we study the following problem:ut = r▽.(lnσ(1 + u)▽u)+(1+u)lnβ(1+u),in D× (0,T),δu/δn= (1+u) lnα(1+u),on δD×(0,T),u(x,0) = u0(x)>0,in-D,where D∈RN is a bounded domain with smooth boundary δD,N≥2.It is proved that if β-1≥α-1>σ≥0, the positive solution u(x,t) blow up globally in -D under suitable assumption on initial data u0(x): Furthermore, upper bound of “blow-up timeand upper estimate of “blow-up rateare given.

关键词： 35K05 35K57 35K55

作者: Juntang Ding Shengjia Li

作者单位: School of Mathematical Sciences Shanxi University Taiyuan, Shanxi 030006, P.R. China

会议类型: 国际会议

会议名称: Fourth International Conference on Impulsive and Hybrid Dynamical Systems(ICIHDS 2007)(第四届国际脉冲和混合动力系统学术会议)

会议地点: 南宁

会议语种:英文

在线出版日期: 2007-07-20（万方平台首次上网日期，不代表论文的发表时间）