Analysis, Dynamical Systems and History

The main research lines of this group are: Analysis, Dynamical Systems, History and Epistemology of Mathematics, and their interdisciplinary applications. The group is composed by 14 PhD’s and 2 doctoral students. Senior members supervise research work at Master, Doctoral and Post-Doc levels.

Analysis

• Existence, regularity and asymptotic behaviour of solutions of evolutive non- linear systems of partial differential equations or variational or quasivariational inequalities
• Global asymptotic stability of an equilibrium point of impulsive neural network models with infinite delay
• Stability and development of stabilizers with different properties for control systems
• Well-posedness issues for the Cauchy problem associated to nonlinear evolution equations of dispersive type with low regularity data; stabilization issues and unique continuation property of the solutions

Dynamical Systems

• Study of the asymptotic behaviour of stochastic dynamical systems at the level of the hydrodynamics, fluctuations, correlations and characterization of the uni- versality classes of Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ)
• Ergodic theory on Heisenberg groups and applications to exponential sums
• Stability and Morse decompositions of non-deterministic systems
• Classification and characterization of bidimensional elementary cellular automata dynamics
• Applications to engineering and social sciences
• Production of interactive material for general public and schools in dynamical systems and applied mathematics 

History and Epistemology of Mathematics
 
• 19th-century European mathematics and reform of the Portuguese educational system
• 18th-century European mathematics and its reception in Portugal