Mathematical analysis

Research group 

Strani Marta, Associate Professor

Research topics

Analysis of partial differential equations 

We are interested in the study of properties of solutions of partial derivative equations.
A first aspect is the study of the asymptotic behavior, for long times, of the solutions of some evolutionary PDEs with nonlinear diffusions. Particular attention is devoted to mean-curvature type diffusions, which find application, for example, in biophysics, chemical physics, population genetics and mathematics of ecology.
Another aspect concerns the study of the behavior of solutions of boundary problems for partial differential equations when, for example, the domain where the problem is defined, the boundary conditions, or the differential operator itself are perturbed.

Phase transition in gradient flow equations

We are interested in the study of partial differential equations of gradient flow type, with particular attention to equations that emerge in mathematical physics to describe the phenomenon of phase transitions (Allen-Cahn and Cahn-Hilliard equations). The study of such multiscale phenomena (fast-slow dynamics) is done mainly through the study of the energy associated to the system.

Potential theory and integral operators

By means of potential theory, boundary problems for some differential operators (e.g., the Laplacian) can be reduced to integral equations by representing the solutions in terms of integral operators. We are interested in studying the properties of such integral operators and associated nonlinear operators. These results are then applied to the study of perturbation problems for boundary problems.

Last update: 19/02/2025