论文标题
两阶段Stefan问题的相位转移区域的边界可控性
Boundary controllability of phase-transition region of a two-phase Stefan problem
论文作者
论文摘要
一个人证明，在$ \ ooo \ subset \ rr^d $，$ d = 1,2,3，$在结束时间$ t $的情况下，Neumann Boundare Contearner $ U $可控制的两阶段Stefan问题的移动接口。 The phase-transition region is a mushy region $\{σ^u_t;\ 0\le t\le T\}$ of a modified Stefan problem and the main result amounts to saying that, for each Lebesque measurable set $\ooo^*$ with positive measure, there is $u\in L^2((0,T)\times\pp\ooo)$ such that $ \ ooo^*\subsetσ^u_t。$ $ to to to to to to to to to to to to to carleman的不等式和kakutani固定点定理，使用了最佳控制方法。
One proves that the moving interface of a two-phase Stefan problem on $\ooo\subset\rr^d$, $d=1,2,3,$ is controllable at the end time $T$ by a Neumann boundary controller $u$. The phase-transition region is a mushy region $\{σ^u_t;\ 0\le t\le T\}$ of a modified Stefan problem and the main result amounts to saying that, for each Lebesque measurable set $\ooo^*$ with positive measure, there is $u\in L^2((0,T)\times\pp\ooo)$ such that $\ooo^*\subsetσ^u_T.$ To this aim, one uses an optimal control approach combined with Carleman's inequality and the Kakutani fixed point theorem.
