NONLINEAR EVOLUTION OF THE STRESS-DRIVEN MORPHOLOGICAL INSTABILITY INA 2-DIMENSIONAL SEMIINFINITE SOLID

We consider the nonlinear evolution of the stress-driven morphological instability on the surface of a two dimensional semi-infinite solid. We track the branch of steady state solutions numerically and find tha t the solution branch terminates. The surface shape at the point of te rmination has a cusp singularity that points into the solid. We also c onsider the time-dependent evolution of the instability from small dis turbances as a function of disturbance wavenumber. We find that the fo rmation of singular grooves in the solid is a general feature of the n onlinear evolution of the instability. Various physical factors which may affect formation of the singularity are discussed.