A qualitative description of microstructure formation and coarsening phenomena for an evolution equation

We provide a qualitative description of microstructure formation and coarsening phenomena for the solutions of a singularly perturbed fourth order evolution equation arising in the study of phase transitions. In particular we study stationary and traveling wave solutions and we construct a class of approximate solution which mimics the principle features of the dynamics. Finally we present several simulations in order to illustrate the results.