VAIN-HOPES:
“VArIational methods and Numerical techniques: sHape Optimization and nonlinear Partial differential EquationS”

Abstract

The goal of this project is advancing the knowledge of mathematical problems that model a variety of scientific applications, e.g., in areas ranging from biology to material sciences, structural mechanics and theoretical physics, but share as a key property the variational structure. The main research lines of the project, with intertwined aspects and methodologies, will be directed toward

- the analytical and numerical study of spectral (and shape) optimization problems,
- the analysis of singular perturbations phenomena,
- the investigation of the long-term behavior of discrete dynamical systems.
The final scientific ambition is to enlarge the set of existing analytical and computational tools, with the long- term objective of providing a strong support to applications based on the selected mathematical models. The project also provides an opportunity to foster collaboration among people working in complementary areas of mathematics, in order to pursue the investigation from a multidisciplinary point of view, to promote the research activity of PhD and PostDoc students in a promising area, and to strengthen the collaboration with other institutions.