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 time”and upper estimate of “blow-up rate”are given.