EVENTO
THE GEVREY CLASS OF THE EULER-BERNOULLI BEAM MODEL
Tipo de evento: Exame de Qualificação
Eliminating the vibration effect of elastic structures is an important topic in materials science and the way in which these structures are built directly influences the process of suppressing the effect of vibrations. Thus, it is increasingly necessary to study such a phenomenon by addressing structures with more than one type of material. In this way, the work to be presented develops a result that is rarely exposed in the literature of a structure with two materials. We study the semigroup associated with the Euler-Bernoulli beam model with localized and discontinuous dissipation. We assume that the beam is composed of two materials, one subinterval of the beam has elastic material and the other subinterval has a damping mechanism of the Kelvin-Voigt type, then, we have a viscoelastic material. Using functional analysis tools and semigroup theory we prove that the model the corresponding semigroup is immediately differentiable and also has the Grevey's regularity. In particular, the model is exponentially stable, has the linear stability property, and has the smoothing effect property over the initial condition taken in the operator's domain.BIBLIOGRAFIA: A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. 3 Island Press, 1992. E. Klaus-Jochen and R. Nagel, One-parameter semigroups for linear evolution equations., ser. Graduate texts in mathematics. New York: Springer, 2000.K. Liu and Z. Liu, Exponential decay of energy of the Euler-Bernoulli beam with locally distributed Kelvin-Voigt damping, SIAM Journal on Control and Optimization, vol. 36, pp. 10861098, 05 1998.S. W. Taylor, Gevrey regularity of solutions of evolution equations and boundary controllability, Ph.D. Dissertation, School of Mathematics, 1989, 182 pp.Z. Liu and S. Zheng, Semigroups associated with dissipative systems. Chapman &Hall/CRC, 1999.Para assistir acesse: https://us02web.zoom.us/j/85339883105?pwd=VWdSQ0FPdWd4eWE4Zmp6Wjc4anQzUT09
Data Início: 09/12/2020 Hora: 13:00 Data Fim: 09/12/2020 Hora: 17:00
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Webinar
Aluno: Bruna Thaís Silva Sozzo - -
Orientador: Jaime E. Muñoz Rivera - LNCC - UFRJ / Brasil - LNCC
Participante Banca Examinadora: Alexandre Loureiro Madureira - Laboratório Nacional de Computação Científica - LNCC Antônio André Novotny - LNCC - LNCC Marcelo Moreira Cavalcanti - UEM / Brasil - UEM Pablo Javier Blanco - Laboratório Nacional de Computação Científica - LNCC
