### Abstract

A system of partial differential equations with integral terms which take into account hereditary effects is considered. The system describes a behaviour of thermoviscoelastic plate with Berger's type of nonlinearity. The hereditary effect is taken into account both in the temperature variable and in the bending one. The main goal of the paper is to analyze the passage to the singular limit when memory kernels collapse into the Dirac mass. In particular, it is proved that the solutions to the system with memory are close in some sense to the solutions to the corresponding memory-free limiting system. Besides, the upper semicontinuity of the family of attractors with respect to the singular limit is obtained.

Original language | English (US) |
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Pages (from-to) | 305-336 |

Number of pages | 32 |

Journal | Journal of Mathematical Physics, Analysis, Geometry |

Volume | 6 |

Issue number | 3 |

State | Published - Dec 1 2010 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematical Physics
- Geometry and Topology

### Cite this

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*Journal of Mathematical Physics, Analysis, Geometry*, vol. 6, no. 3, pp. 305-336.

**On singular limit and upper semicontinuous family of attractors of thermoviscoelastic Berger Plate.** / Potomkin, Mykhailo.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On singular limit and upper semicontinuous family of attractors of thermoviscoelastic Berger Plate

AU - Potomkin, Mykhailo

PY - 2010/12/1

Y1 - 2010/12/1

N2 - A system of partial differential equations with integral terms which take into account hereditary effects is considered. The system describes a behaviour of thermoviscoelastic plate with Berger's type of nonlinearity. The hereditary effect is taken into account both in the temperature variable and in the bending one. The main goal of the paper is to analyze the passage to the singular limit when memory kernels collapse into the Dirac mass. In particular, it is proved that the solutions to the system with memory are close in some sense to the solutions to the corresponding memory-free limiting system. Besides, the upper semicontinuity of the family of attractors with respect to the singular limit is obtained.

AB - A system of partial differential equations with integral terms which take into account hereditary effects is considered. The system describes a behaviour of thermoviscoelastic plate with Berger's type of nonlinearity. The hereditary effect is taken into account both in the temperature variable and in the bending one. The main goal of the paper is to analyze the passage to the singular limit when memory kernels collapse into the Dirac mass. In particular, it is proved that the solutions to the system with memory are close in some sense to the solutions to the corresponding memory-free limiting system. Besides, the upper semicontinuity of the family of attractors with respect to the singular limit is obtained.

UR - http://www.scopus.com/inward/record.url?scp=84883802593&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883802593&partnerID=8YFLogxK

M3 - Article

VL - 6

SP - 305

EP - 336

JO - Journal of Mathematical Physics, Analysis, Geometry

JF - Journal of Mathematical Physics, Analysis, Geometry

SN - 1812-9471

IS - 3

ER -