Evolution equation for a thin epitaxial film on a deformable substrate

We consider a continuum model for the evolution of an epitaxially strained dislocation-free thin solid film on a deformable substrate in the absence of vapor deposition. By using a thin-film approximation we derived a nonlinear evolution equation. We examined the nonlinear evolution equation and found that there is a critical film thickness below which every film thickness is stable and a critical wave number above which every film thickness is stable. Preliminary numerical results indicate that the equation possesses island-like steady state solutions.