The project deals with the development of innovative techniques for the numerical solution of evolutionary partial differential equations, concentrating in particular on the numerical treatment of mathematical models described by hyperbolic and kinetic equations.

A broad range of physical systems is governed by hyperbolic systems of conservation or balance laws. Among these we recall the classical fields of gas dynamics and shallow water equations describing free surface waves, or more recent models describing traffic flow. Likewise, kinetic models, originally introduced to provide an accurate statistical description of a large collections of gas particles, can be effectively adopted to describe other behaviors, such as pedestrian flow, swarming, and other kinds of social dynamics. In several models, control problems can be effectively described by Hamilton-Jacobi type equation, whose mathematical structure has strong analogies with the structure of hyperbolic systems of conservation laws.

The project will focus on some specific aspects, developing new techniques for the numerical solution of such models, analyzing their mathematical properties and applying them to cases of high impact.

e.cristiani@iac.cnr.it