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Mathematical Analysis, Modelling, and Applications

The activity in mathematical analysis is mainly focussed on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry are also developed.The activity in mathematical modelling is oriented to subjects for which the main technical tools come from mathematical analysis. The present themes are multiscale analysis, mechanics of materials, micromagnetics, modelling of biological systems, and problems related to control theory.The applications of mathematics developed in this course are related to the numerical analysis of partial differential equations and of control problems. This activity is organized in collaboration with MathLab for the study of problems coming from the real world, from industrial applications, and from complex systems.

Dynamics of vortex-patches

The purpose of this course is to study some dynamical properties of weak solutions to Euler equations in simply-connected domains. A focus will be done on vortex patches which are particular weak solutions where the vorticity is the characteristic functions of a bounded domain. The first part of the course will be devoted to the proof Yudovich's Theorem stating the existence and uniqueness of weak solutions.

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