Departamento de Matemática - UFPB

João Pessoa - PB - 24 e 25 de Julho de 2014

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Programação

Quinta Feira - 24/07/2014

 10:30 - 11:15  -  Eduardo Cerpa (UTFSM - Chile) 11:15 - 12:00  -  Juan Límaco (UFF) ------------------------------ 15:30 - 16:15  -  Diego Souza (US - Espanha) 16:15 - 17:00  -  Alberto Mercado (UTFSM - Chile)

Sexta Feira - 25/07/2014

 10:30 - 11:15  -  Valéria Domingos Cavalcanti (UEM) 11:15 - 12:00  -  Luz de Teresa (UNAM - México)

Títulos e resumos das palestras

Eduardo Cerpa (UTFSM-Chile)
Título: Feedback control of the Korteweg-de Vries equation
Resumo: This talk is concerned with the stabilization problem of the Korteweg-de Vries equation posed on a bounded interval. The design of some feedback control laws stabilizing the system is presented. Three different tools are used: a damping method, a Gramian-based approach and the Backstepping method.

Juan Límaco (UFF)
Titulo: Controle do N-dimensional modelo de Ladyzhenskaya-Smagorinsky con N-1 controles escalares em um domínio de control arbitrário.
Resumo: Nesta palestra abordaremos o estudo da controlabilidade nula local do modelo de Ladyzhenskaya-Smagorinsky com N-1 controles escalares, sendo arbitrário o domínio onde atua o controle. Nós seguimos as ideias de um recente trabalho de Carreño-Guerrero que trata deste problema para o sistema de Navier-Stokes com N-1 controles.

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Diego Souza (US-Espanha)
Título: On the uniform control of some $\alpha$-models
Resumo: This talk deals with the internal and boundary controllability results of the so called Leray-$\alpha$ model of turbulence. This is a regularized variant of the Navier-Stokes system ($\alpha$ is a small positive parameter), the usual transport term is regularized with an operator that depends on $\alpha$. In the limit $\alpha$ tending to $0^+$, we find the classical Navier-Stokes system. The main aim of the talk is to prove that the Leray-$\alpha$ systems are locally null controllable, with controls uniformly bounded with respect to $\alpha$. We also prove that, if the initial data are sufficiently small, the controls converge as $\alpha \to 0^+$ to a null control of the Navier-Stokes equations. We also discuss some additional results and open questions.

Título: Controllability of Schrodinger equations.
Resumo: The problem of controllability of Schrödinger equations by means of a control supported in a region not satisfying the classical geometrical control condition is addressed. We prove the controllability of a cascade system of two linear n-dimensional Schrödinger equations, using one single control. The proof is based on Carleman estimates with degenerate weights.

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Valéria Domingos Cavalcanti (UEM)
Título: Intrinsic decay rate estimates for the wave equation with competing viscoelastic and frictional dissipative effects
Resumo: Wave equation defined on a compact Riemannian manifold (M; g) subject to a combination of locally distributed viscoelastic and frictional dissipations is discussed. The viscoelastic dissipation is active on the support of a(x) while the frictional damping affects the portion of the manifold quantified by the support of b(x) where both a(x) and b(x) are smooth functions. Assuming that a(x) + b(x) > 0 for all x in M and that the relaxation function satisfies certain nonlinear differential inequality, it is shown that the solutions decay according to the law dictated by the decay rates corresponding to the slowest damping. In the special case when the viscoelastic effect is active on the entire domain and the frictional dissipation is differentiable at the origin, then the overall decay rates are dictated by the viscoelasticity.

Luz de Teresa (UNAM- México)
Título: A Carleman inequality for a one dimensional degenerate parabolic equations with first order terms.
Resumo: In this conference we present a Carleman estimate for the one dimensional degenerate parabolic equation: v_t + (x^{\alpha}v_{x})_{x} =F_0+(x^{\beta/2}F_1)_x, (x,t) \in (0,1) \times (0,T), where $\alpha \in [0,2)$, $\beta \ge \alpha$ and $F_0,F_1\in L^2((0,1)\times (0,T))$ and give some controllability consequences.

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Todas as palestras acontecerão na sala de reuniões do Departamento de Matemática

Para mais informações contactar:

Fágner Araruna -  Este endereço de email está protegido contra piratas. Necessita ativar o JavaScript para o visualizar.
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