Several physical and natural phenomena are characterized on one hand by the presence of different temporal and spatial scales, on the other by the presence of contacts among different components through rough (fractal) interfaces; in all these phenomena the information flows from a smaller to a larger scale or viceversa. Different fields of application are biology, human respiration, engineering disciplines. Our aim is to propose mathematical models to investigate these phenomena as well as their numerical approximation. The lack of regularity of the underlying fractal structures requires new tools and techniques for PDEs . Taking into account our expertise in the study of scalar BVPs in irregular domains we will focus on vector BVPs in fractal domains which involve in the boundary conditions integrodifferential operators.
Our research will be divided in 4 main topics:
1) HEAT DIFFUSION WITH NONLOCAL DYNAMICAL BOUNDARY CONDITIONS IN FRACTAL BOUNDARIES
2) QUASILINEAR PROBLEMS
3) VECTOR ANALYSIS ON FRACTAFOLDS: NAVIER-STOKES EQUATIONS and MAXWELL EQUATIONS IN FRACTAL DOMAINS: THEORY AND APPROXIMATIONS
4) FRACTIONAL DIFFUSION ACROSS FRACTAL INTERFACES
