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.

Controllability for discrete systems with a finite control set

Chitour Y, Piccoli B. Controllability for discrete systems with a finite control set. Math. Control Signals Systems 14 (2001) 173-193 [Internet]. 2001 . Available from: http://hdl.handle.net/1963/3114

Weak convergence of measures on spaces of semicontinuous functions.

Dal Maso G, De Giorgi E, Modica L. Weak convergence of measures on spaces of semicontinuous functions. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 79 (1985), no. 5, 98-106 [Internet]. 1985 . Available from: http://hdl.handle.net/1963/463

Parametrized curves in Lagrange Grassmannians

Zelenko I, Chengbo L. Parametrized curves in Lagrange Grassmannians. C. R. Math. 345 (2007) 647-652 [Internet]. 2007 . Available from: http://hdl.handle.net/1963/2560

Singular perturbation models in phase transitions for second order materials

Chermisi M, Dal Maso G, Fonseca I, Leoni G. Singular perturbation models in phase transitions for second order materials. Indiana Univ. Math. J. 60 (2011) 367-409 [Internet]. 2011 . Available from: http://hdl.handle.net/1963/3858

Axial symmetry of some steady state solutions to nonlinear Schrödinger equations

Gui C, Malchiodi A, Xu H, Yang P. Axial symmetry of some steady state solutions to nonlinear Schrödinger equations. Proc. Amer. Math. Soc. 139 (2011), 1023-1032 [Internet]. 2011 . Available from: http://hdl.handle.net/1963/4100

Biological Fluid Dynamics, Non-linear Partial Differential Equations

DeSimone A, Alouges F, Lefebvre A. Biological Fluid Dynamics, Non-linear Partial Differential Equations. In: Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554. Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554. ; 2009. Available from: http://hdl.handle.net/1963/2630

A model of crack propagation based on viscous approximation

Lazzaroni G, Toader R. A model of crack propagation based on viscous approximation. [Internet]. 2010 . Available from: http://hdl.handle.net/1963/4110

Hybrid optimal control: case study of a car with gears

D'Apice C, Garavello M, Manzo R, Piccoli B. Hybrid optimal control: case study of a car with gears. Int. J. Control 76 (2003) 1272-1284 [Internet]. 2003 . Available from: http://hdl.handle.net/1963/3022

S^2 type parametric surfaces with prescribed mean curvature and minimal energy

Caldiroli P, Musina R. S^2 type parametric surfaces with prescribed mean curvature and minimal energy. In: Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77. Nonlinear equations : methods, models and applications (Bergamo, 2001) / Daniela Lupo, Carlo D. Pagani, Bernhard Ruf, editors. - Basel : Birkhäuser, 2003. - (Progress in nonlinear differential equations and their applications; 54). - p. 61-77. Birkhauser; 2001. Available from: http://hdl.handle.net/1963/1605

On the Euler-Lagrange equation for a variational problem

Bianchini S. On the Euler-Lagrange equation for a variational problem. Discrete Contin. Dynam. Systems A 17 (2007) 449-480 [Internet]. 2007 . Available from: http://hdl.handle.net/1963/1792

Mathematics