In questo lavoro si considera il seguente problema di "nonequilibrium phase-change":
\[
\begin{cases}
C\frac{\partial u}{\partial t}-k\frac{\partial^{2}u}{\partial x^{2}}=0,0<x<1,0<t<T,\\
u(0,t)=h(t),u(1,t)=h(t),\\
u(x,0)=u(x),s(0)=s_{0},\\
s(0)=s_{0},k\left[\frac{\partial u(s(t)+,t)}{\partial x}-\frac{\partial u(s(t)-,t)}{\partial x}\right]=L\dot{s(t)=} & Lg(u(s(t),t))
\end{cases}
\]
e si dimostra l'esistenza di sue soluzioni deboli o classiche sotto
certe condizioni. In thls paper we consider the following problem of nonequilibrlum phase-change:
\[
\begin{cases}
C\frac{\partial u}{\partial t}-k\frac{\partial^{2}u}{\partial x^{2}}=0,0<x<1,0<t<T,\\
u(0,t)=h(t),u(1,t)=h(t),\\
u(x,0)=u(x),s(0)=s_{0},\\
s(0)=s_{0},k\left[\frac{\partial u(s(t)+,t)}{\partial x}-\frac{\partial u(s(t)-,t)}{\partial x}\right]=L\dot{s(t)=} & Lg(u(s(t),t))
\end{cases}
\]
and prove the existence of its weak or classical solutions under some
conditions.
