Many physical and biological phenomena take place across disordered and wild media. For instance, diffusion processes in physical membranes, the current flow across rough electrodes in electrochemistry, diffusion of sprays in the lungs are transport phenomena which occur, from the geometrical point of view, across irregular layers. Irregular structures provide appropriate frameworks to irrigation models, bronchial systems, root infiltration, tree foliage and other kinds of applications where surface effects are dominant. The role of surface roughness also in contact mechanics is relevant to processes ranging from adhesion to friction wear and lubrication. It also has a deep impact on applied sciences, including coating technology and design of microelectro-mechanical systems.
In particular, DIFFUSION PROCESSES ON IRREGULAR STRUCTURES could be applied to get a deeper insight in many physical phenomena such as particle diffusion, spin diffusion, and diffusion regimes in electrochemistry.
In this framework, fractal layers or boundaries provide new interesting setting to describe wild or irregular media and bodies in which "boundaries" are "large" while bulk is "small". Hence, in the theory of boundary value problems, a new perspective emerges to model phenomena in which the surface effects are enhanced.
The present project is concerned with the study of Partial Differential Equations arising as models of diffusion processes on irregular structures: domains with non-smooth boundaries, fractal boundaries and fractal layers.
Problems on irregular structures are particularly significant because they provide us with a deep insight into an arena where Euclidean and fractal concepts and techniques cross each other. Such an interbreeding is indeed the marking trait of the present research project.
