Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary

Gaudiello, Antonio; Mel'nyk, Taras A.

doi:10.1016/j.jde.2018.07.002

Cited by 26 publications

(25 citation statements)

References 29 publications

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“…In [3], unfolding operators for locally periodic oscillating domain has been defined, again the base of the oscillations is flat. In the context of homogenization of non-linear problems in oscillating domains, one can see [22], where authors have analysed asymptotic behavior of a monotone type operator with nonlinear signorini boundary condition. In [32], non-linear parabolic problem using asymptotic expansion has been studied.…”

Section: Introductionmentioning

confidence: 99%

Oscillating PDE in a rough domain with a curved interface: Homogenization of an Optimal Control Problem

Nandakumaran

Sufian

2021

ESAIM: COCV

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Homogenization of an elliptic PDE with periodic oscillating coefficients and an associated optimal control problems with energy type cost functional is considered. The domain is a 3-dimensional region (method applies to any $n$ dimensional region) with oscillating boundary, where the base of the oscillation is curved and it is given by a Lipschitz function. Further, we consider a general elliptic PDE with oscillating coefficients. We also include very general type cost functional of Dirichlet type given with oscillating coefficients which can be different from the coefficient matrix of the equation. We introduce appropriate unfolding operators and approximate unfolded domain to study the limiting analysis. The present article is new in this generality.

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Section: Introductionmentioning

confidence: 99%

Oscillating PDE in a rough domain with a curved interface: Homogenization of an Optimal Control Problem

Nandakumaran

Sufian

2021

ESAIM: COCV

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“…Homogenization of oscillating boundaries with fixed amplitude is widely studied and we refer to the following main papers: [1], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [15], [21], [22], [23], [24], [26], [27], [28], [29], [30], [31], [32], [41] [42], [45], [46], [47], [48], and [53].…”

Section: Introductionmentioning

confidence: 99%

A Two-Dimensional Electrostatic Model of Interdigitated Comb Drive in Longitudinal Mode

Gaudiello¹,

Lenczner²

2020

SIAM J. Appl. Math.

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A periodic homogenization model of the electrostatic equation is constructed for a comb drive with a large number of fingers and whose mode of operation is in-plane and longitudinal. The model is obtained in the case where the distance between the rotor and the stator is of an order ε α , α ≥ 2, where ε denotes the period of distribution of the fingers. The model derivation uses the two-scale convergence technique. Strong convergences are also established. This allows us to find, after a proper scaling, the limit of the electrostatic force applied to the rotor in the longitudinal direction.

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“…Amirat et al have considered Laplace equation and studied asymptotic behavior and derived error estimates. For homogenization of nonlinear problems in oscillating domains, one can look into the work of Gaudiello and Mel'nyk, where they have studied a homogenization of a monotone problem with nonlinear Signorini boundary conditions. Mel'nyk studied nonlinear parabolic problem using asymptotic expansion.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of a boundary optimal control problem on a general branched structure

Aiyappan

Nandakumaran

Sufian

2019

Math Methods in App Sciences

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We consider an optimal control problem posed on a domain with a highly oscillating smooth boundary where the controls are applied on the oscillating part of the boundary. There are many results on domains with oscillating boundaries where the oscillations are pillar-type (non-smooth) while the literature on smooth oscillating boundary is very few. In this article, we use appropriate scaling on the controls acting on the oscillating boundary leading to different limit control problems, namely, boundary optimal control and interior optimal control problem. In the last part of the article, we visualize the domains as a branched structure, and we introduce unfolding operators to get contributions from each level at every branch. KEYWORDS asymptotic analysis, homogenization, optimal control, oscillating boundary domain, unfolding operator MSC CLASSIFICATION 80M35; 80M40; 49J20; 35B27 Math Meth Appl Sci. 2019;42:6407-6434.wileyonlinelibrary.com/journal/mma

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Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary

Cited by 26 publications

References 29 publications

Oscillating PDE in a rough domain with a curved interface: Homogenization of an Optimal Control Problem

Oscillating PDE in a rough domain with a curved interface: Homogenization of an Optimal Control Problem

A Two-Dimensional Electrostatic Model of Interdigitated Comb Drive in Longitudinal Mode

Asymptotic analysis of a boundary optimal control problem on a general branched structure

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