Variational approach to homogenization of doubly-nonlinear flow in a periodic structure

Nandakumaran, A. K.; Visintin, Augusto

doi:10.1016/j.na.2015.02.010

Cited by 2 publications

(1 citation statement)

References 19 publications

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“…There is also a large amount of literature on the homogenization with oscillating boundaries, which has tremendous applications as well (for example, , , and ). For some recent work on oscillating boundaries, see and . For general literature in homogenization, we refer to and the reference therein.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of Neumann periodic optimal boundary control problem

Nandakumaran

Prakash

Sardar

2016

Math Methods in App Sciences

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An optimal boundary control problem in a domain with oscillating boundary has been investigated in this paper. The controls are acting periodically on the oscillating boundary. The controls are applied with suitable scaling parameters. One of the major contribution is the representation of the optimal control using the unfolding operator. We then study the limiting analysis (homogenization) and obtain two limit problems according to the scaling parameters. Another notable observation is that the limit optimal control problem has three controls, namely, a distributed control, a boundary control, and an interface control.

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Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of Neumann periodic optimal boundary control problem

Nandakumaran

Prakash

Sardar

2016

Math Methods in App Sciences

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The weighted energy-dissipation principle and evolutionary Γ-convergence for doubly nonlinear problems

Liero

Melchionna

2019

ESAIM: COCV

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We consider a family of doubly nonlinear evolution equations that is given by families of convex dissipation potentials, nonconvex energy functionals, and external forces parametrized by a small parameter ε. For each of these problems, we introduce the so-called weighted energy-dissipation (WED) functional, whose minimizers correspond to solutions of an elliptic-in-time regularization of the target problems with regularization parameter δ. We investigate the relation between the Γ-convergence of the WED functionals and evolutionary Γ-convergence of the associated systems. More precisely, we deal with the limits δ → 0, ε → 0, as well as δ + ε → 0 either in the sense of Γ-convergence of functionals or in the sense of evolutionary Γ-convergence of functional-driven evolution problems, or both. Additionally, we provide some quantitative estimates on the rate of convergence for the limit ε → 0, in the case of quadratic dissipation potentials and uniformly λ-convex energy functionals. Finally, we discuss a homogenization and a dimension reduction problem as examples of application.

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Variational approach to homogenization of doubly-nonlinear flow in a periodic structure

Cited by 2 publications

References 19 publications

Asymptotic analysis of Neumann periodic optimal boundary control problem

Asymptotic analysis of Neumann periodic optimal boundary control problem

The weighted energy-dissipation principle and evolutionary Γ-convergence for doubly nonlinear problems

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