Evolutionary problems: analysis techniques and construction of numerical solutions
| Componente | Categoria |
|---|---|
| Corrado Mascia | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Andrea Davini | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Elisabetta Carlini | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Giuseppe Visconti | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Andrea Terracina | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Silvia Noschese | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Flavia Lanzara | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Maurizio Falcone | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
| Agnese Pacifico | Dottorando/Assegnista/Specializzando componente non strutturato del gruppo di ricerca / PhD/Assegnista/Specializzando member non structured of the research group |
| Matteo Piu | Dottorando/Assegnista/Specializzando componente non strutturato del gruppo di ricerca / PhD/Assegnista/Specializzando member non structured of the research group |
| Antonio Siconolfi | Componenti strutturati del gruppo di ricerca / Structured participants in the research project |
This project studies evolutionary problems in several fields, with the tools of numerical analysis, scientific computing and mathematical analysis. The common denominator is the need to address complexity in evolutionary PDEs.
We will study evolution equations in random media, well posedness at junctions and the construction of solutions on networks. We will consider hyperbolic and parabolic equations as limits of kinetic models or arising from control problems, Mean Field Games or population dynamics.
Particular care will be devoted to the construction of new numerical methods to solve multiscale PDEs and to the use of accurate numerical computations to gain insight into the solution of complex models, in order to drive rigorous mathematical analysis from simple toy problems to more complex equations.
Numerical methods developed within this project range from Monte Carlo methods for kinetic problems, implicit methods for hyperbolic PDEs, Semi Lagrangian schemes, Reduced basis methods for PDEs in high dimensional spaces.
The theory and the new numerical techniques will be applied to several problems with a strong impact, such as vehicular traffic models, in particular considering the effects of autonomous vehicles, and problems from biology, in particular cancer growth in healthy tissues, and epidemiological models.