一种自由边界上有源的STEFAN问题解的收敛性质

THE CONVERGENCE OF THE SOLUTIONS TO THE STEFAN PROBLEM WITH SOURCE ON FREE BOUNDARY

讨论自由边界条件为uε(hε(t),t)=0,-xuε(hε(t),t)=λ+εh′ε(t)的Stefan问题,得到了解关于ε的一致估计,从而证明了对任何T>0,存在0<γ1<1,自由边界hε(t)在C1+γ1/2[0,T]中收敛.

A Stefan problem with the conditions uε(hε(t),t)=0,-xuε(hε(t),t)=λ+εh′ε(t) in free boundary is discussed. A uniform estimate of the solutions with respect to ε>0 is obtained and it is shown, that when ε approaches zero, hε(t) converges to h(t) in C1+γ1/?2 for any T>0(0>γ1<1).