An optimal control problem in a tubular thin domain with rough boundary

Nakasato, Jean Carlos; Pereira, Marcone C.

doi:10.1016/j.jde.2021.12.021

Journal of Differential Equations

2022

DOI: 10.1016/j.jde.2021.12.021

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An optimal control problem in a tubular thin domain with rough boundary

Jean Carlos Nakasato

Marcone C. Pereira

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Cited by 6 publications

References 33 publications

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Elliptic equations in weak oscillatory thin domains: Beyond periodicity with boundary‐concentrated reaction terms

Barbosa,

Villanueva‐Pesqueira

2024

Math Methods in App Sciences

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In this paper, we analyze the limit behavior of a family of solutions of the Laplace operator with homogeneous Neumann boundary conditions, set in a two‐dimensional thin domain that presents weak oscillations on both boundaries and with terms concentrated in a narrow oscillating neighborhood of the top boundary. The aim of this problem is to study the behavior of the solutions as the thin domain presents oscillatory behaviors beyond the classical periodic assumptions,including scenarios such as quasi‐periodic or almost‐periodic oscillations. We then prove that the family of solutions converges to the solution of a one‐dimensional limit equation capturing the geometry and oscillatory behavior of boundary of the domain and the narrow strip where the concentration terms take place. In addition, we include a series of numerical experiments illustrating the theoretical results obtained in the quasi‐periodic context.

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Elliptic equations in weak oscillatory thin domains: Beyond periodicity with boundary‐concentrated reaction terms

Barbosa,

Villanueva‐Pesqueira

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

Homogenization of the non-isothermal, non-Newtonian fluid flow in a thin domain with oscillating boundary

Nakasato,

Pažanin

2023

Z. Angew. Math. Phys.

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Homogenization of Semi-linear Optimal Control Problems on Oscillating Domains with Matrix Coefficients

Nandakumaran,

Sufian,

Thazhathethil

2024

Appl Math Optim

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An optimal control problem in a tubular thin domain with rough boundary

Cited by 6 publications

References 33 publications

Elliptic equations in weak oscillatory thin domains: Beyond periodicity with boundary‐concentrated reaction terms

Elliptic equations in weak oscillatory thin domains: Beyond periodicity with boundary‐concentrated reaction terms

Homogenization of the non-isothermal, non-Newtonian fluid flow in a thin domain with oscillating boundary

Homogenization of Semi-linear Optimal Control Problems on Oscillating Domains with Matrix Coefficients

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