===== PDE 9: Iceberg equation =====
 \[u_t = \nu u_{xx},\quad 0 < x < h(t),\quad t > 0\]   

 \[h(0) = 0  \]

 \[u(0,t) = f(t),\quad t > 0\]  

 \[u(h(t),t) = 0,\quad t > 0  \]

 \[\frac{dh(t)}{dt}=-\alpha\,u_x(h(t),t),\quad t>0 \]


In this equation both  \(u(x,t)\) are \(h(t)\) unknowns. 
Find appropriate boundary conditions and parameter values  \(\nu, \alpha, f(t)  \) from physical considerations.

**Google**: Stefan problem, free boundary, moving boundary

**Challenges**: free/moving boundary.