数学物理学报(英文版) ›› 1998, Vol. 18 ›› Issue (3): 315-325.
林支桂
Lin Zhigui
摘要: This paper deals with the blow-up properties of solutions to semilinear heat equation ut-uxx=up in (0, 1)×(0, T) with the Neumann boundary condition ux(0, t)=0, ux(1, t)=1 on[0, T). The necessary and sufficient conditions under which all solutions to have a finite time blow-up and the exact blow-up rates are established. It is proved that the blow-up will occur only at the boundary x=1. The asymptotic behavior near the blow-up time is also studied.