Título: Spectrum of differential operators with elliptic adjoint on a scale of localized Sobolev spaces.
Data: 14/06/2023
Horário: 12:00h
Local: C-116
Palestrante: Luís Salge (UFRJ)
Resumo: In this work we present a complete study about the spectrum of a constant coefficients differential operator of order m a positive integer, a(D), whose adjoint a(D)* is elliptic, seen as a pseudo-differential operator on an interval I. The best conclusions we obtain are when we consider the Laplace operator on an interval I defined on a Sobolev space of order 2, i.e., H^{2}_{0}(I) with the topology induced by the L^{2}_{loc} which is a Fréchet space. For it, we calculate its closure and their types of spectrum.
Título: On the optimal control of non-Newtonian fluids.
Data: 12/07/2023
Horário: 12:00h
Local: C-116
Palestrante: Fernanda Cipriano (Universidade Nova de Lisboa)
Resumo:
We discuss the optimal control problems of flows governed by the incompressible deterministic and stochastic third grade fluid equations with Navier-slip boundary conditions.
After recalling the results on the well-posedness of the state equations, we study the existence and the uniqueness of solution to the linearized state and adjoint equations. Furthermore, we present a stability result for the state, and show that the solution of the linearized equation coincides with the Gâteaux derivative of the control-to-state mapping. Next, we prove the existence of an optimal solution and establish the first order optimality conditions.
In the deterministic case, an uniqueness result of the coupled system constituted by the state equation, the adjoint equation and the first order optimality condition is established, under sufficiently large intensity of the cost.
This is a joint work with Y. Tahraoui.
Bibliography:
[1] A. Almeida, N. Chemetov and F. Cipriano, Uniqueness for optimal control problems of two-dimensional second grade fluids. EJDE, Vol. 2022, No. 22, 1-12 (2022)
[2] N. Chemetov, F. Cipriano, Optimal control for two-dimensional stochastic second grade fluids. Stochastic Processes Appl., 128, Issue 8, 2710-2749 (2018)
[3] F. Cipriano, P. Didier, S. Guerra, Well-posedness of stochastic third grade fluid equation. J. Diff. Eq., 285, 496-535 (2021)
[4] Y. Tahraoui and F. Cipriano, Optimal control of two dimensional third grade fluids. J. Math. Anal. Appl., 523, 127032, (2023)
[5] Y. Tahraoui and F. Cipriano, Local strong solutions to the stochastic third grade fluid equations with Navier Boundary conditions,
https://doi.org/10.48550/
Título: "The limit shape of the critical front profile for vanishing diffusion in Born-Infeld models"
Data: 26/04/2023
Horário: 12:00h
Local: C-116
Palestrante: Maurizio Garrione (Politecnico di Milano)
Resumo: We deal with traveling fronts for reaction-diffusion models where the diffusive term is of relativistic (Born-Infeld) type. We show that, in case the reaction term is monostable, the critical front connecting 0 and 1 sharpens on one side only, near the equilibrium 0. The presence of a convective term may alter this picture, leading to fully sharp or fully regular limit profiles, as will be briefly shown. The technique relies on a careful analysis of the associated first-order reduction.
Titulo: Propriedades matemáticas do fluxo de espuma em meios porosos.
Palestrante: Luis Fernando Lozano G. (LAMAP - UFJF)
Data: 09/08/2023
Horário: 12h
Sala: C-116
Resumo: AQUI
Palestra 1
Titulo: Stabilization of a time delayed for a generalized dispersive system.
Palestrante: Fernando A. Gallego (Universidad Nacional de Colombia)
Data: 08/02/2023
Horário: 11:00
Local: sala C-119
Resumo: In this talk we study the asymptotic behavior of the solution of the time–delayed higher order dispersive systems posed in the real line. Under suitable assumptions on the time delay coefficients we prove that the system under consideration is exponentially stable in two different ways. First, if the coefficient of the delay term is bounded from below by a positive constant, we use the Lyapunov approach to prove that the energy associated to the solution of the higher order dispersive system decays exponentially. After that, we extend this result to the case in which the coefficient of the undelayed feedback is also indefinite. Both problems are investigated when the exponent p in the nonlinear term ranges over the interval [1, 2j) where 2j + 1 is the order of the dispersive system.
Palestra 2
Titulo: A coupling approach to quantify the transportation Wasserstein path-distance between heat equation and the Goldstein--Kac telegraph equation.
Palestrante: Gerardo Barrera (University of Helsinki)
Data: 08/02/2023
Horário: 12:00
Local: sala C-119
Resumo: In this talk, I will present a non-asymptotic process level control between the so-called telegraph process (a.k.a. Goldstein-Kac equation) and a diffusion process with suitable diffusivity constant (explicit) via a transportation Wasserstein path-distance with quadratic average cost.
We stress that the telegraph process solves a partial linear differential equation of the hyperbolic type for which explicit computations can be carried by in terms of Bessel functions. In the present talk, I will discuss the coupling approach, which is a robust technique that can be used for more general PDEs. The proof is done via the interplay of the following couplings: coin-flip coupling, synchronous coupling and the celebrated Komlós-Major-Tusnády coupling. In addition, non-asymptotic estimates for the corresponding L^p time average are given explicitly.
The talk is based on joint work with Jani Lukkarinen, University of Helsinki, Finland."
