- 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.
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- Project code: 2017KKJP4X
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