Comportamento Assintótico da Equação de Bernoulli-Euler com Dissipação Localizada e Efeito de Inércia Rotacional
DOI:
https://doi.org/10.5540/tema.2007.08.02.0309Abstract
Neste trabalho estudamos o comportamento assintótico da energia do problema de valor inicial e de fronteira associado com a equa cão de Bernoulli-Euler com efeito de inércia rotacional e um termo não linear dissipativo localizado em uma vizinhança da fronteira do domínio. O comportamento assintótico da energia no tempo é obtido com taxas de decaimento explícitas. Esse resultado é obtido utilizando-se o lema de Nakao, estimativas de energia via multiplicadores localizados e um argumento de “compacidade-unicidade”baseado no princípio de continuação única. O comportamento assintótico é válido para a equação de Bernoulli-Euler sem efeito de inércia rotacional ou para a equa cão de placas com efeito de inércia rotacional.References
[1] F. Alabau-Boussouira, Convexity andWeighted Integral Inequalities for Energy Decay Rates of Nonlinear Dissipative Hyperbolic Systems, Applied Mathematics and Optimization, 51, (2005), 67-91.
R.C. Charão, E. Bisognin, V. Bisognin, A.F. Pazoto, Asymptotic behavior of a Bernoulli-Euler type equation with nonlinear localized damping, Contributions to Nonlinear Analysis - Progress in nonlinear partial differential equations and their applications, 66, (2005), 67-91.
R. Gulliver, I. Lasiecka, W. Littman, R. Triggiani, The Case for Differential Geometry in the Control of Single and Coupled PDES: The Structural Acoustic Chamber, IMA Volumes in Mathematics and its Applications, 137, (2004), 73-182.
J.U. Kim, A unique continuation property of a beam equation with variable coefficients, in estimation and control of distributed parameter sustems, International Series of Numerical Mathematics, 100, (1991), 197-205.
J.L. Lions, Exact controllability, stabilization and perturbations for distributed systems, SIAM Rev., 30,(1988), 1-68.
M. Nakao, Decay of solutions of the wave equation with a local nonlinear dissipation, Math. Ann., 305, (1996), 403-417.
M. Tucsnak, Semi-internal stabilization for a non-linear Bernoulli-Euler equation,Mathematical Methods in the Applied Sciences, 19, (1996), 897-907.
M. Tucsnak, Stabilization of Bernoulli-Euler beam by means of a pointwise feedback force, SIAM J. Control Optim., 39, (2000) 1160-1181.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish in this journal agree to the following terms:
Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.
Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).
This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
author. This is in accordance with the BOAI definition of open access
Intellectual Property
All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.