Optimal L 1-Control in Coefficients for Dirichlet Elliptic Problems: W-Optimal Solutions

Kogut, Peter I.; Leugering, Günter

doi:10.1007/s10957-011-9840-4

Cited by 22 publications

(17 citation statements)

References 9 publications

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“…As the two, opposing layers are brought into contact by an input device, current flows between the two conductive films allowing the controller to identify where the touch position is located and then feed that to the computer software processing the event. Figure 17b shows the additional contact resistance resulting from the impact of two rough conducting surfaces with a thin insulating layer separating them as one might find in touch panels made from CNTs or AgNWs 253. The contact resistance is largely influenced by the impurities in the solution based transparent conductors such that the overall roughness and peak to valley values become very important in device operation.…”

Section: Applicationsmentioning

confidence: 99%

Emerging Transparent Electrodes Based on Thin Films of Carbon Nanotubes, Graphene, and Metallic Nanostructures

Hecht¹,

Hu²,

Irvin³

2011

Advanced Materials

2,061

1,767

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Transparent electrodes are a necessary component in many modern devices such as touch screens, LCDs, OLEDs, and solar cells, all of which are growing in demand. Traditionally, this role has been well served by doped metal oxides, the most common of which is indium tin oxide, or ITO. Recently, advances in nano-materials research have opened the door for other transparent conductive materials, each with unique properties. These include CNTs, graphene, metal nanowires, and printable metal grids. This review will explore the materials properties of transparent conductors, covering traditional metal oxides and conductive polymers initially, but with a focus on current developments in nano-material coatings. Electronic, optical, and mechanical properties of each material will be discussed, as well as suitability for various applications.

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Section: Applicationsmentioning

confidence: 99%

Emerging Transparent Electrodes Based on Thin Films of Carbon Nanotubes, Graphene, and Metallic Nanostructures

Hecht¹,

Hu²,

Irvin³

2011

Advanced Materials

2,061

1,767

View full text Add to dashboard Cite

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“…To the authors' best knowledge, the existence of optimal solutions for the aforementioned problem is an open question. Moreover, only few papers deal with optimal control problems for the degenerate partial differential equations (see for example ).…”

Section: Introductionmentioning

confidence: 99%

Optimal and approximate boundary controls of an elastic body with quasistatic evolution of damage

Kogut

Leugering

2014

Math Methods in App Sciences

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Communicated by M. BrokateIn this paper, we study an optimal control problem for the mixed boundary value problem for an elastic body with quasistatic evolution of an internal damage variable. We suppose that the evolution of microscopic cracks and cavities responsible for the damage is described by a nonlinear parabolic equation. A density of surface traction p acting on a part of boundary of an elastic body is taken as a boundary control. Because the initial boundary value problem of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions, we deal with the solvability of this problem in the class of weak variational solutions. Using the convergence concept in variable spaces and following the direct method in calculus of variations, we prove the existence of optimal and approximate solutions to the optimal control problem under rather general assumptions on the quasistatic evolution of damage.

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“…In this case, the precise answer for the question of existence or nonexistence of optimal solutions heavily depends on the class of chosen admissible controls. Using the direct method in the calculus of variations, we discuss the solvability of this optimal control problem in the class of the so-called -admissible solutions (see, for instance, [1,2]). It should be emphasized that in contrast to the paper [3], we do not make use of any relaxations for the original optimal control problem.…”

Section: Introductionmentioning

confidence: 99%

“…It is worth noticing that even though numerous articles (see, for instance, [13][14][15][16][17][18] and references therein) are devoted to variational and nonvariational approaches to problems related to linear and nonlinear elliptic systems, only few deal with optimal control problems for degenerate partial differential equations and variational inequalities (see e.g., [1,2,[19][20][21][22][23]).…”

Section: Introductionmentioning

confidence: 99%

On an Optimal -Control Problem in Coefficients for Linear Elliptic Variational Inequality

Kupenko

Manzo

2013

Abstract and Applied Analysis

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We consider optimal control problems for linear degenerate elliptic variational inequalities with homogeneous Dirichlet boundary conditions. We take the matrix-valued coefficients in the main part of the elliptic operator as controls in . Since the eigenvalues of such matrices may vanish and be unbounded in , it leads to the “noncoercivity trouble.” Using the concept of convergence in variable spaces and following the direct method in the calculus of variations, we establish the solvability of the optimal control problem in the class of the so-called -admissible solutions.

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Optimal L 1-Control in Coefficients for Dirichlet Elliptic Problems: W-Optimal Solutions

Cited by 22 publications

References 9 publications

Emerging Transparent Electrodes Based on Thin Films of Carbon Nanotubes, Graphene, and Metallic Nanostructures

Emerging Transparent Electrodes Based on Thin Films of Carbon Nanotubes, Graphene, and Metallic Nanostructures

Optimal and approximate boundary controls of an elastic body with quasistatic evolution of damage

On an Optimal -Control Problem in Coefficients for Linear Elliptic Variational Inequality

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