Analysis

NOVA Math > Research Groups > Analysis

About

The research of the Analysis group spans several branches of mathematical analysis and its applications: calculus of variations, dynamical systems, numerical methods for ordinary and partial differential equations, stochastic and deterministic partial differential equations, harmonic analysis and operator theory, mathematical models in physical and biological sciences. The research related to operator theory and harmonic analysis is mainly focused on the study of Fredholm properties of convolution-type operators (like Toeplitz or Wiener-Hopf operators) in Banach function spaces. One of the important themes studied by the group is related to applications of stochastic differential equations in modelling of fluid mechanics. Mathematical modelling of infectious diseases (including COVID 19 and the Dengue fever) is another topic of active research by the group.

Oleksiy Karlovych

Analysis Coordinator

Team

Publications

Optimal control of two dimensional third grade fluids
2023, Journal of Mathematical Analysis and Applications, Tahraoui,Y;Cipriano,F
A large deviation principle for fluids of third grade
2023, STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, Almeida,A;Cipriano,F
A lower estimate for weak-type Fourier multipliers
2022, COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, Karlovich,A;Shargorodsky,E
On an analogue of a theorem by Astala and Tylli
2022, ARCHIV DER MATHEMATIK, Karlovich,A;Shargorodsky,E
On the weak convergence of shift operators to zero on rearrangement-invariant spaces
2022, REVISTA MATEMATICA COMPLUTENSE, Karlovych,O;Shargorodsky,E
On interpolation of reflexive variable Lebesgue spaces on which the Hardy-Littlewood maximal operator is bounded
2022, GEORGIAN MATHEMATICAL JOURNAL, Diening,L;Karlovych,O;Shargorodsky,E
UNIQUENESS FOR OPTIMAL CONTROL PROBLEMS OF TWO-DIMENSIONAL SECOND GRADE FLUIDS
2022, ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, Almeida,A;Chemetov,NV;Cipriano,F
Finite Difference Schemes with Non-uniform Time Meshes for Distributed-Order Diffusion Equations
2022, Lecture Notes in Networks and Systems, Morgado,ML;Rebelo,M;Ferr√°s,LL
ON THE ESSENTIAL NORMS OF SINGULAR INTEGRAL OPERATORS WITH CONSTANT COEFFICIENTS AND OF THE BACKWARD SHIFT
2022, Proceedings of the American Mathematical Society, Series B, Karlovych,O;Shargorodsky,E
A generalised distributed-order Maxwell model
2022, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Ferras,LL;Morgado,ML;Rebelo,M

Projects

CoSysM3 - Mathematical Modelling of Multi-scale Control Systems: applications to human diseases
FCT - Fundação para a Ciência e a Tecnologia, I.P., Paula Patrício, Paulo Doutor, magda Rebelo, Fabio...
Projeção do Impacte das medidas Não-farmacológicas de Controlo e mitigação da epidemia de COVID-19 em Tempo ReaL
FCT - Fundação para a Ciência e a Tecnologia, I.P., Paula Patrício
Contribuciones a los modelos estocasticos en epidemias
Agéncia Estatal de Investigación (Spain), Fabio Chalub
Dispersive Evolution Equations
FCT and CAPES (Portugal & Brazil), Filipe Oliveira
Prémio “Estímulo à Investigação 2016”
Fundação Calouste Gulbenkian, Fernanda Cipriano
Game theory and epidemiology
FCT - Fundação para a Ciência e a Tecnologia, I.P., Paula Rodrigues, Fabio Chalub, Paulo Doutor, Maria...
Variational problems in variable exponent Sobolev spaces
FCT - Fundação para a Ciência e a Tecnologia, I.P., Ana Margarida Ribeiro, Rita Ferreira and Oleksiy...
MiMaMathematics in the Making
Lifelong Learning Programme of the European Union Project (EU), Susana Baptista, Nelson Chibeles Martins,...
Degenerate elliptic and parabolic equations and its applications to front propagation propagation
FCT - Fundação para a Ciência e a Tecnologia, I.P., Fabio Chalub
Nonlinear dynamics of ordinary differential equations and applications
FCT - Fundação para a Ciência e a Tecnologia, I.P., Rogério Ferreira Martins