Analytical validation of a 2+1 dimensional continuum model for epitaxial growth with elastic substrate

Abstract

An analytical validation is obtained for the evolution equation $$h_t=\Delta [{\mathcal{F}}^{-1}(-aE\mathcal{F}(h))-r/h^2-\Delta h],$$ introduced in {\cite{TS}} by W.T. Tekalign and B.J. Spencer to describe the heteroepitaxial growth of a two-dimensional thin film on an elastic substrate. In the expression above, $h$ denotes the surface height of the film, $\mathcal{F}$ is the Fourier transform, and $a$, $E$, $r$ are positive material constants. Existence, uniqueness, and Lipschitz regularity in time for weak solutions are proved, under suitable assumptions on the initial datum.

This paper has been withdrawn due to major changes