Boundary controllability of phase-transition region of a two-phase Stefan problem

One proves that the moving interface of a two-phase Stefan problem on Ω⊂Rd, d=1,2,3, is controllable at end time T by Neumann boundary controller u. The phase-transition region mushy {σtu;0≤t≤T} modified and main result amounts to saying that, for each Lebesgue measurable set Ω∗ with positive measure, there u∈L2((0,T)×∂Ω) such Ω∗⊂σTu. To this aim, one uses an optimal control approach combined Carleman’s inequality Kakutani fixed point theorem.