| Abstract: | In this paper, the following one-phase Stefan problem is considered: u
1=u
xx
+f(u,t) in Q(T), u(x,0)=u
0(x), 0⩽x⩽l
0,
u(l(t),t)=0, 0 < t ⩽T, l'(t)=-u
x
(l(t),t),l(0)=l
0, where Q
l(T)={(x,t)|0<x<l(t), 0<t≦T} and l
0>0. It is proved that when the solution is blow-up in a finite time s(u
o), and u
0(x) is not a constant, then the free boundary will not be blow-up and the blow-up set is contained in the interval 0,l
0). Moreover, when f(u,t)=u
1+μ for some μ>0, every blow-up point is isolated.
This work is supported by National Natural Science Foundation of China |
