# Spectral Analysis of Linear Models of Viscoelasticity

## Abstract

In this paper, we examine Volterra integrodifferential equations with unbounded operator coefficients in Hilbert spaces. Equations considered are abstract hyperbolic equations perturbed by terms containing Volterra integral operators. These equations can be realized as partial integrodifferential equations that appear in the theory of viscoelasticity (see [2, 5]), as Gurtin–Pipkin integrodifferential equations (see [1, 7]) that describe finite-speed heat transfer in materials with memory. They also appear in averaging problems for multiphase media (Darcy’s law.

- Authors:

- M. V. Lomonosov Moscow State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771289

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 5; Conference: International symposium on differential equations, Perm (Russian Federation), 17-18 May 2016; 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:
- 97 MATHEMATICAL METHODS AND COMPUTING; ELASTICITY; HEAT TRANSFER; HILBERT SPACE; INTEGRO-DIFFERENTIAL EQUATIONS; MATHEMATICAL OPERATORS; MATHEMATICAL SOLUTIONS

### Citation Formats

```
Vlasov, V. V., E-mail: vikmont@yandex.ru, and Rautian, N. A., E-mail: nrautian@mail.ru.
```*Spectral Analysis of Linear Models of Viscoelasticity*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3766-4.

```
Vlasov, V. V., E-mail: vikmont@yandex.ru, & Rautian, N. A., E-mail: nrautian@mail.ru.
```*Spectral Analysis of Linear Models of Viscoelasticity*. United States. doi:10.1007/S10958-018-3766-4.

```
Vlasov, V. V., E-mail: vikmont@yandex.ru, and Rautian, N. A., E-mail: nrautian@mail.ru. Tue .
"Spectral Analysis of Linear Models of Viscoelasticity". United States. doi:10.1007/S10958-018-3766-4.
```

```
@article{osti_22771289,
```

title = {Spectral Analysis of Linear Models of Viscoelasticity},

author = {Vlasov, V. V., E-mail: vikmont@yandex.ru and Rautian, N. A., E-mail: nrautian@mail.ru},

abstractNote = {In this paper, we examine Volterra integrodifferential equations with unbounded operator coefficients in Hilbert spaces. Equations considered are abstract hyperbolic equations perturbed by terms containing Volterra integral operators. These equations can be realized as partial integrodifferential equations that appear in the theory of viscoelasticity (see [2, 5]), as Gurtin–Pipkin integrodifferential equations (see [1, 7]) that describe finite-speed heat transfer in materials with memory. They also appear in averaging problems for multiphase media (Darcy’s law.},

doi = {10.1007/S10958-018-3766-4},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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