# Optimal Control Problem for Two-Layer Elastic Body with Crack

## Abstract

We establish the unique solvability of the equilibrium problem for a two-layer body. One layer contains a crack, whereas the second one is glued along its edge to the first layer in such a way that to cover one of the crack ends. In the case, where the second layer is a rigid plate, we show that the problem with a rigid patch is the limit of problems with elastic patches as the rigidity parameter tends to infinity. We also study the optimal control problem with the exterior forces acting on both layers taken for the control function.

- Authors:

- Lavrent’ev Institute of Hydrodynamics SB RAS (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771396

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; 97 MATHEMATICAL METHODS AND COMPUTING; CRACKS; ELASTICITY; EQUILIBRIUM; LAYERS; OPTIMAL CONTROL

### Citation Formats

```
Pyatkina, E. V., E-mail: dusya-pyatkina@mail.ru.
```*Optimal Control Problem for Two-Layer Elastic Body with Crack*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3735-Y.

```
Pyatkina, E. V., E-mail: dusya-pyatkina@mail.ru.
```*Optimal Control Problem for Two-Layer Elastic Body with Crack*. United States. doi:10.1007/S10958-018-3735-Y.

```
Pyatkina, E. V., E-mail: dusya-pyatkina@mail.ru. Sun .
"Optimal Control Problem for Two-Layer Elastic Body with Crack". United States. doi:10.1007/S10958-018-3735-Y.
```

```
@article{osti_22771396,
```

title = {Optimal Control Problem for Two-Layer Elastic Body with Crack},

author = {Pyatkina, E. V., E-mail: dusya-pyatkina@mail.ru},

abstractNote = {We establish the unique solvability of the equilibrium problem for a two-layer body. One layer contains a crack, whereas the second one is glued along its edge to the first layer in such a way that to cover one of the crack ends. In the case, where the second layer is a rigid plate, we show that the problem with a rigid patch is the limit of problems with elastic patches as the rigidity parameter tends to infinity. We also study the optimal control problem with the exterior forces acting on both layers taken for the control function.},

doi = {10.1007/S10958-018-3735-Y},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 1,

volume = 230,

place = {United States},

year = {2018},

month = {4}

}

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