Coarsening in surface growth models without slope selection

We study conserved models of crystal growth in one dimension [$\partial_t z(x,t) =-\partial_x j(x,t)$] which are linearly unstable and develop a mound structure whose typical size L increases in time ($L=t^n$). If the local slope ($m={\mathrm{\partial }}_{x}z$) increases indefinitely, $n$ depends on the exponent $\gamma$ characterizing the large $m$ behaviour of the surface current $j$ ($j = 1/|m|^\gamma$):$n=1/4$for$1< \gamma <3$and$n=(1+\gamma)/(1+5\gamma)$for$\gamma>3$.