We study problems of formation and evolution of patterns for fourth order differential equations.
In particular we are interested in the study of stationary solutions, traveling waves and self-similar solutions. Through the study of these solutions we want to describe qualitative phenomena of dynamics such as the presence of various time scales and coarsening.
Furthermore, we are interested in the effects produced by stochastic and non-autonomous perturbations on the qualitative behavior of the solutions.
The methods used range from the theory of ordinary equations to the theory of evolution problems, from the theory of attractors to that of random dynamical systems.