MAT/05 Analysis

Calculus of Variations and Geometric Measure Theory
Shape and spectral optimization, discrete and continuous models,
variational convergences, semicontinuity, relaxation, homogenization,
non-local interactions, geometric problems, curve evolution, theory of perimeters,
theory of currents, fine structure of sets and functions,
continuum mechanics and phase transitions, transport
problems, analysis and geometric measure theory in Carnot spaces.
People
Giovanni Alberti
Giuseppe Buttazzo
Maria Stella Gelli
Valentino Magnani
Matteo Novaga
Emanuele Paolini
Vincenzo Maria Tortorelli
Dario Trevisan

 

Hyperbolic Equations, Dispersive Equations and Kirchhoff Equations
Cauchy problems for strictly or weakly hyperbolic equations and systems
with low regularity coefficients. Local solvability problems for non-principal
operators.
Local/global uniqueness/existence for Cauchy problems, asymptotic
behavior of solutions (scattering theory), statistical behavior of
solutions through construction of invariant measures.
First/second order evolution equations with a dissipative term (linear
or nonlinear). Optimal regularity of solutions and characterization of
asymptotic behavior of solutions. Existence and uniqueness for the
Kirchhoff equation.
People
Ferruccio Colombini 
Vladimir Georgiev
Marina Ghisi
Massimo Gobbino
Nicola Visciglia
 

Equations of Fluid Dynamics
Existence, regularity and asymptotic behavior of solutions. Applications
for turbulence, geophysical flows and biomedicine problems. Study of
time-periodic or stationary flows for non-Newtonian fluids in external
domains and domains with a finite number of cylindrical outputs.
Applications to Emodynamic.
People
Luigi Berselli
Carlo Romano Grisanti
Elisabetta Chiodaroli

Dynamic Systems and Ergodic Theory
Statistical properties of dynamics, entropy, spectral properties, links
with number theory and computational methods.
People
Claudio Bonanno
Carlo Carminati
Stefano Galatolo
 

Nonlinear Analysis
Nonlinear elliptic partial differential equations, with particular
attention to the role of nonlinearity in problems of existence,
multiplicity, qualitative properties and concentration of solutions
phenomena. Critical or almost critical issues and Yamabe type equations.
Blow up methods and solution building, bifurcation and
perturbed singular problems. Existence of solitons, orbital and dynamic stability
problems in evolutionary problems.
People
Marco Gipo Ghimenti
Pietro Majer
Claudio Saccon

Control Theory
Utility maximization problems originating from the economic growth
theory: existence of optimal control under state constraints, study of
the Hamilton-Jacobi-Bellman equation. Energy minimization problems
originating from the physics of non-equilibrium states: existence of
optimal control and study of a non-standard Riccati equation.
Linear-quadratic control problems in Hilbert spaces using
semigroup theory: applications to hyperbolic-parabolic
physical-mathematical problems.
People
Paolo Acquistapace
Francesca Bucci (università di Firenze)
Fausto Gozzi (LUISS)