The project START is focused on the development and study of mathematical tools for the modeling of diffusion in non-classical settings. Diffusion is the net movement from a region of higherconcentration to a region of lower concentration. The concept of diffusion is present in all the fields of applied sciences, including physics (particle diffusion), chemistry (motion of atoms, molecules, and ions according to a gradient), biology, sociology, and economics (diffusion of populations of individuals, ideas, and price values). In the classical models for diffusion, every direction plays the same role (isotropic regime) and the motion occurs locally, namely to points that are spatially near. Clearly, such models are not sufficient for the description of the rich variety of real-world phenomena: for example, in the spread of a wildfire or cancer, diffusion is driven by nonlocal features (sparks moved by the wind, metastasis) or particular directions are preferred by the dynamics (anisotropic regime); also, evolution might behave chaotically, as for example in fluid diffusion and chemical reactions.

The goal of this project is the study of diffusion problems for nonlocal phenomena in nonisotropic settings and in thin structures. We will tackle such problems with the instruments of mathematical analysis, studying appropriate topics and Partial Differential Equations, both in the continuous and discrete setting, the last being useful for computer-oriented solvers.