n optimal control problem in a tubular thin domain with rough boundar

Autor(es)

Nakasato, Jean Carlos ^[1] ; Pereira, Marcone Correa ^[2]

Afiliação do(s) autor(es)

^[1] Univ Zagreb, Fac Sci, Dept Math, Bijenicka Cesta 30, Zagreb - Croatia

^[2] Univ Sao Paulo, Dept Matemat Aplicada, IME, Rua Matao 1010, Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 313, p. 188-243, MAR 15 2022.
• Citações Web of Science: 0

Resumo

In this paper we analyze the asymptotic behavior of a control problem set by a convection-reaction diffusion equation with mixed boundary conditions and defined in a tubular thin domain with rough boundary. The control term acts on a subset of the rough boundary where a Robin-type boundary condition and a catalyzed reaction mechanism are set. The reaction mechanism depends on a parameter alpha is an element of R. Such parameter establishes different regimes which also depend on the profile and geometry of the tube defined by a periodic function g : R-2 bar right arrow R. We see that, if partial derivative(2)g is not null (that is, when g really depends on the second variable), then three regimes with respect to alpha are established: alpha < 2, alpha = 2 (the critical value) and alpha > 2. On the other hand, if partial derivative(2)g equivalent to 0, similar regimes are obtained but now with a different critical value. Indeed, if partial derivative(2)g equivalent to 0, then the critical value is achieved at alpha = 1. For each one of these six regimes, we obtain the asymptotic behavior of the control problem when the cylindrical thin domain degenerates to the unit interval. We show that the problem is asymptotically controllable just when alpha assumes the critical values. Our analysis is mainly performed using the periodic unfolding method adapted to cylindrical coordinates in R-3. (c) 2021 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 20/14075-6 - Sistemas dinâmicos e seus atratores sob perturbação
• Beneficiário: Alexandre Nolasco de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 20/04813-0 - Análise assintótica e qualitativa de equações integro-diferenciais
• Beneficiário: Marcone Corrêa Pereira
• Modalidade de apoio: Auxílio à Pesquisa - Regular