具有非线性边界条件半线性热方程解的爆破估计(英)

Blow-up Estimates of Solutions to Semilinear Heat Equations with Nonlinear Boundary Condition

本文考虑具有非线性边界条件-u_x（0，t）=u^q（0，t）在（0，T）半线性热方程u_t-u_(xx)=u^p在（0，∞）×（0，T）的正解．在初值的一些单调性假定下证明了c（T-t）^(-t)≤supu（x，t）≤C（T-0）^(-r)其中r=1／（p-1）如户＞2q-1且r=1／[2（q-1）]如p≤2q-1.

This paper deals with positive solutions to semilinear heat equation u_t＝u_(xx)＋u^qin（0,∞）×(0.T）with the nonlinear boundary condition -u_x (0,t)=u^q(0,t) on (0,T). We prove that c(T-t)^(-r)≤supu（x，t）≤C（T-t）~r under some monotonicity assumptions on the initial value, where γ=1/(p-1) if q＞2q-1 and γ=1/[2（q-)] if p≤2q-1.