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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

in Analysis:
  • 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.

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