一些 n 維半線性波方程解的暴破速度與暴破常數研究(II)

Abstract

於此計畫 吾人欲將n維半線性波方程之初始-邊界值問題 (SL) u」 – Δu = u2 in [0,T) × Ω,u = 0 on [0,T] × . Ω, u(0,·) = f ..H2(Ω), u(0,·) = g ..H1(Ω) 解之暴破集與暴破速度及暴破常數研究清楚 起碼給出估算.

In this Project we want to know the blow-up set of the solution to the initial value problem for the semi-linear wave equation in n-space dimension,n?4, (SL) u . u = u2 in [0,T)  ,u = 0 on [0,T]   , u(0,) = f ....2(), u(0,) = g ..C1(), where T ..(0,?] and ..nR ,n?4, is a bounded domain on which the divergent theorem can be applied. We shall also compute the blow-up rate and blow-up constant of the solution for the initial value problem for the semi-linear wave equation (SL).