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Seminário 08 de Março
5 05America/Sao_Paulo abril 05America/Sao_Paulo 2023 @ 08:00 - 17:00
Seminário EDP e Matemática Aplicada
March 08, 2023 – 14h (Brazil)
Streaming: Youtube Channel
About Seminars
Seminars are used to explore specific topics in more depth, present research results, projects and studies, and brainstorm ideas with others interested in the same subject.
Featured Talks & Speakers
Iván Moyano
Université Côte D’Azur (Nice, France)
14:00h – 14:40h
Controllability and stabilization of PDE control systems with crucial quadratic terms
We are interested in the controllability and asymptotic stabilization of some nonlinear partial differential equations where the quadratic term plays a crucial role in the sense that neither the controllability nor the asymptotic stabilization holds without these terms. We show that in this case, for the controllability, one may need more time than expected by the speed of propagation to control these systems. For the stabilization, we construct explicit time-varying feedback laws which lead to exponential stabilization for the natural weighted norm.
Iván Moyano
Université Côte D’Azur (Nice, France)
14:50h – 15:30h
Uncertainty principles in control theory of PDEs
In this talk we review some classical and recent results relating the uncertainty principles for the Laplacian with the controllability and stabilisation of some linear PDEs. The uncertainty principles for the Fourier transforms state that a square integrable function cannot be both localised in frequency and space without being zero, and this can be further quantified resulting in unique continuation inequalities in the phase spaces. Applying these ideas to the spectrum of the Laplacian on a compact Riemannian manifold, Lebeau and Robbaino obtained their celebrated result on the exact controllability of the heat equation in arbitrarily small time. The relevant quantitative uncertainty principles known as spectral inequalities in the literature can be adapted to a number of different operators, including the Laplace-Beltami operator associated to C^1 metrics or some Schödinger operators with long-range potentials, as we have shown in recent results in collaboration with Gilles Lebeau (Nice) and Nicolas Burq (Orsay), with a significant relaxation on the localisation in space. As a consequence, we obtain a number of corollaries on the decay rate of damped waves with rough dampings, the simultaneous controllability of heat equations with different boundary conditions and the controllability of the heat equation with rough controls.
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.
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