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Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana DuranteTaras A. Mel’nyk — 2012

ESAIM: Control, Optimisation and Calculus of Variations

We consider quasilinear optimal control problems involving a thick two-level junction which consists of the junction body and a large number of thin cylinders with the cross-section of order 𝒪( ). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary conditions...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana DuranteTaras A. Mel’nyk — 2012

ESAIM: Control, Optimisation and Calculus of Variations

We consider quasilinear optimal control problems involving a thick two-level junction which consists of the junction body and a large number of thin cylinders with the cross-section of order 𝒪( ). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. ...

Asymptotic approximation for the solution to a semi-linear elliptic problem in a thin aneurysm-type domain

Taras A. Mel’nykArsen V. Klevtsovskiy — 2017

Open Mathematics

A semi-linear boundary-value problem with nonlinear Robin boundary conditions is considered in a thin 3D aneurysm-type domain that consists of thin curvilinear cylinders that are joined through an aneurysm of diameter 𝓞(ε). Using the multi-scale analysis, the asymptotic approximation for the solution is constructed and justified as the parameter ε → 0. Namely, we derive the limit problem (ε = 0) in the corresponding graph, define other terms of the asymptotic approximation and prove energetic and...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana DuranteTaras A. Mel’nyk — 2012

ESAIM: Control, Optimisation and Calculus of Variations

We consider quasilinear optimal control problems involving a thick two-level junction which consists of the junction body and a large number of thin cylinders with the cross-section of order 𝒪( ). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. ...

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