Analysis and Applications
The group of Analysis and Applications is composed by 26 doctors and 8 doctoral students, having in addition the collaboration of 3 external members with doctorates. Doctors supervise research work at Master, Doctoral and Post-Doc levels.
The main research lines in this group are: Analysis, Numerical Analysis, Hypercomplex Analysis, Dynamical Systems, History of Mathematics, and their interdisciplinary applications.
Main topics of research are
- to prove existence and to study regularity and asymptotic behavior of solutions of nonlinear evolutive equations or systems of variational and quasi-variational inequalities;
- to find sufficient conditions for the global stability of functional differential equations with or without impulses;
- to study peak-effect in linear control systems;
- to study the existence of close to equilibrium solutions for the system of PDE’s in the frame of the kinetic theory of chemically reacting gases;
- to study the dynamics and linear stability of reactive shocks and combustion waves in kinetic theory of chemically reacting gases;
- to study Q-classes, when the determinant of the matrix Q is zero and to apply to various factorization problems and to the study of Toeplitz operators with symbol in a Q-class.
in Numerical Analysis:
- to study a new class of matrix and a new pseudo inverse to produce efficient preconditioning matrix;
- to introduce a new class of very high-order finite volume scheme for mixte problems such as the stokes problem taking into account the div-grad duality;
- to carry out realistic and high resolution simulation of Tsunami using the MOOD procedure;
- to study and solve integral equations as well as the spectral problem associated.
in Hypercomplex Analysis:
- to obtain analytic and geometric characterization of holomorphic functions in higher dimensional Euclidean spaces;
- to develop root-finding algorithms in quaternion context.
in Dynamical Systems:
- to study the cohomology of certain algebraic actions on quotients of Heisenberg groups over the reals or over non-Archimedean local fields;
- to obtain pde’s with boundary conditions from the hydrodynamic limit and fractional spde’s from the fluctuations of interacting particle systems;
- to study dynamical systems from geometric and ergodic viewpoints;
- to study the formation of spatio-temporal patterns in dynamic fields with time-varying input.
in History of Mathematics:
- to characterize algebra and analytic geometry in Portugal from the reform of Jesuit mathematical teaching in 1692 to the aftermath of the University reform of 1772;
- to study Portuguese mathematical manuscripts from José Anastácio da Cunha (1744-1787) and/or from his students.
The group of Analysis and Applications results from a recent internal reorganisation of CMAT that brought together all members of the group Analysis, Dynamical Systems and History
, some members of the group Geometry, Topology and Mathematical Physics
and some members of the group Computational Mathematics and Applications