Seminar in EDP and Applied Mathematics
May 15, 2024 – 14h (Brazil)
Streaming: Youtube Channel | SEMINARIO DE EDP E MATEMATICA APLICADA
Event
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About Seminars
Our Online Seminar is one of the most important events in Brazil, it has been held since August 2020, every Wednesday at 2 pm, Brasília time, with a frequency of 14 days. Two 40-minute lectures are presented in each session. Our speakers are world-renowned mathematicians from Europe, the United States and South America.
Featured Talks & Speakers
About Organization
Juan Limaco – UFF – Brazil (Coordenador);
Mauro Rincon – UFRJ – Brazil
Max Souza – UFF – Brazil;
Sandra Malta – LNCC – Brazil
Marcelo Cavalcanti – UEM – Brazil;
Rui Almeida – UBI – Portugal
Roxana Lopez – UNMSM – Peru;
Diego Souza – U Sevilla – España;
Mauricio Sepulveda – UdeC – Chile;
Roberto Capistrano – UFPE – Brazil.
Our Partners
![Jacques](http://edpemaplicada.uff.br/wp-content/uploads/sites/308/2024/05/Jacques-scaled.jpg)
Jacques Simon
CNRS, France
14:00h – 14:40h
Integration with values in a Neumann space for PDE’s
We It may be useful to use elements in spaces such as L^{p}([0,T] ;L^{q}_{loc}(Ω)) or H^{-1}([0,T]; W^{m,q}(Ω)-weak) … unfortunately they were not yet defined. Theses spaces L^{q}_{loc}(Ω) and W^{m,q}(Ω)-weak are Neumann spaces, that are vector spaces provided with semi-norms that made them separated and sequentially complete.
We will define D'(Ω;E), L^{p}(Ω;E) and W^{m,p}(Ω;E) where E is a Neumann space and Ω is an open set of R^{d}, and we show some applications to PDE’s.
We insist on L^{p}(Ω;E) which is composed of measures: it cannot be composed
of class of almost equal functions because the theory fails, since Egoroff theorem
does not extend if E is not metrisable.
When E is a Banach space and \hat{f} \hat{L}^{p}(Ω;E), that is the space of p-integrable
almost equal functions, then a measure \bar{f} is defined by: for all φ \in K(Ω),
<\bar{f}, φ>=\int_{Ω}\hat{f}φ
We prove that our space L^{p}(Ω;E) is {\bar{f} : \hat{f} \in \hat{L}^{p}(Ω;E)} and that \hat{f}→\bar{f} is an isomorphism. So, our L^{p}(Ω;E) is the true Lebesgue space if E is a Banach space.
![Maher Moakher](http://edpemaplicada.uff.br/wp-content/uploads/sites/308/2024/05/Maher-Moakher.png)
Maher Moakher
National Engineering School at Tunis, University of Tunis El Manar,Tunis
14:50h – 15:30h
Decay estimates for semilinear wave equations with time-dependent time delay
The importance of the cone of symmetric positive-definite matrices can hardly be exaggerated.
Such matrices are omnipresent and play fundamental roles in several disciplines such as
mathematics, numerical analysis, probability and statistics and engineering sciences. Nowadays, as
some applications deliver data that are constrained to live on this set, it has become even more
essential to understand its geometric structure.
Starting from a one-parameter family of potential functions, we introduce Riemannian metrics and
give explicit expressions for the associated geodesics and distance functions. We also use the same
family of potential functions to introduce divergence functions that define the information
geometry. Then, we introduce means of symmetric positive-definite matrices that are based on the
different distance and divergence functions. Some applications of the Riemannian and information
geometries to data processing of symmetric positive-definite matrices will be presented.
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