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

Tiziana Durante; Taras A. Mel’nyk

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 2, page 583-610
- ISSN: 1292-8119

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topDurante, Tiziana, and Mel’nyk, Taras A.. "Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1∗." ESAIM: Control, Optimisation and Calculus of Variations 18.2 (2012): 583-610. <http://eudml.org/doc/277820>.

@article{Durante2012,

abstract = {We consider quasilinear optimal control problems involving a thick two-level junction
Ωε which consists of the junction body
Ω0 and a large number of thin cylinders with the
cross-section of order 𝒪(ε2). 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 depend on parameters ε, α,
β and the thin cylinders from each level are ε-periodically
alternated. Using the Buttazzo–Dal Maso abstract scheme for variational convergence of
constrained minimization problems, the asymptotic analysis (as ε → 0) of
these problems are made for different values of α and β
and different kinds of controls. We have showed that there are three qualitatively
different cases. Application for an optimal control problem involving a thick one-level
junction with cascade controls is presented as well. },

author = {Durante, Tiziana, Mel’nyk, Taras A.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Homogenization; quasilinear optimal control problem; thick multilevel junction; asymptotic behavior; singular perturbation; homogenization},

language = {eng},

month = {7},

number = {2},

pages = {583-610},

publisher = {EDP Sciences},

title = {Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1∗},

url = {http://eudml.org/doc/277820},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Durante, Tiziana

AU - Mel’nyk, Taras A.

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2012/7//

PB - EDP Sciences

VL - 18

IS - 2

SP - 583

EP - 610

AB - We consider quasilinear optimal control problems involving a thick two-level junction
Ωε which consists of the junction body
Ω0 and a large number of thin cylinders with the
cross-section of order 𝒪(ε2). 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 depend on parameters ε, α,
β and the thin cylinders from each level are ε-periodically
alternated. Using the Buttazzo–Dal Maso abstract scheme for variational convergence of
constrained minimization problems, the asymptotic analysis (as ε → 0) of
these problems are made for different values of α and β
and different kinds of controls. We have showed that there are three qualitatively
different cases. Application for an optimal control problem involving a thick one-level
junction with cascade controls is presented as well.

LA - eng

KW - Homogenization; quasilinear optimal control problem; thick multilevel junction; asymptotic behavior; singular perturbation; homogenization

UR - http://eudml.org/doc/277820

ER -

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