Title:

Three-Dimensional Thermo-Visco-Elasticity with the Einstein-Debye (θ3 + θ)-law for the Specific Heat.Global Regular Solvability

Subtitle:

Raport Badawczy = Research Report ; RB/12/2017

Creator:

Pawłow, Irena ; Zajączkowski, Wojciech

Publisher:

Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences

Place of publishing:

Warszawa

Date issued/created:

2017

Description:

37 pages ; 21 cm ; Bibliography p. 35-37

Subject and Keywords:

Existence of global regular solutions ; Istnienie globalnych regularnych rozwiązań ; Kelvin-voigt type materials ; Sobolev spaces with a mixed norm ; Materiały typu kelvina-voigta ; Przestrzenie sobolewa o normie mieszanej ; Thermoviscoelastic system ; Einstein-debye law for specific heat ; System termo-wiskoelastyczny ; Prawo einsteina-debye'a dla ciepła właściwego

Abstract:

In this paper, a three-dimensional thermo-visco-elastic system for Kelvin-Voigtbtype material at small strain is considered. The system involves constantbheat conductivity and the specific heat satisfying the Einstein-Debye (θ3+θ)-law. Such nonlinear law, relevant at relatively low temperatmes, represents the main novelty of the paper. The existence of global regular solutions is proved without small data assumption. The crucial part of the proof is the strictly positive lower bound on the absolute temperature θ. In case of the Debye θ3-law this still remains an unsolved problem. The existence of local in time solution is proved by the Banach successive approximations method. The global a priori estimates are derived with the help of the theory of anisotropic Sobolev spaces with a mixed norm. Such estimates allow to extend the local solution step by step in time.

Relation:

Raport Badawczy = Research Report

Resource type:

Text

Detailed Resource Type:

Report

Source:

RB-2017-12

Language:

eng

Language of abstract:

eng

Rights:

Creative Commons Attribution BY 4.0 license

Terms of use:

Copyright-protected material. [CC BY 4.0] May be used within the scope specified in Creative Commons Attribution BY 4.0 license, full text available at: ; -

Digitizing institution:

Systems Research Institute of the Polish Academy of Sciences

Original in:

Library of Systems Research Institute PAS

Projects co-financed by:

Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.

Access:

Open