Uniqueness classes of solutions of two-phase coefficient inverse Stefan problems (Q2375968)

Sufficient conditions are derived for the functions \(p^k\) (\(k=1,2\)), which are the form \(p(x)\), \(p(u)\), or \(p(x,u)\), to ensure the uniqueness of a solution \((u,\xi,p^1,p^2)\) (if it exists) of the one-dimensional two-phase Stefan problem \(c^k(x,t,u)u_t-(a^k(x,t,u)u_x)_x+b^k(x,t,u)u_x=p^kd^k(x,t,u)\) for \((x,t)\in ](k-1)\xi(t),(k-1)l+(2-k)\xi(t)[\times ]0,T[\), \(\gamma(\xi,t,u)\xi_t =(a(\xi,t,u)u_x)_{x=\xi(t)}+\chi(\xi,t,u)\) for \(0<t<T\), under Dirichlet boundary, initial, and final conditions, where the input data belong to Hölder spaces.