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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


 
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