Thermo-elastic and thermo-piezo-elastic interaction crack type boundary-transmission problems with regard to the microrotation
type: Item
instance of: scholarly article
title: Thermo-elastic and thermo-piezo-elastic interaction crack type boundary-transmission problems with regard to the microrotation
zbMATH Open document ID: 1547.35665
author: O. Chkadua
author: Anna Danelia
published in: Transactions of A. Razmadze Mathematical Institute
publication date: 2024-07-25T00:00:00Z
review text: The authors study a boundary-transmission problem for a composed elastic structure consisting of two contacting bodies occupying two three-dimensional adjacent regions with a common contacting interface, being a proper part of the boundaries of the adjacent regions. The mathematical model, which takes into account coupling effects between thermo-mechanical and electric fields in elastic composites, is based on the Green-Naghdi theory of thermo-piezo-electricity without energy dissipation. This theory permits the thermal waves to propagate only with a finite speed. The system of partial differential equations of pseudo-oscillations is obtained from the corresponding dynamical model by the Laplace transform. Using the potential theory and the method of pseudodifferential equations on manifolds with a boundary, the authors prove the existence, uniqueness and regularity of solutions.
reviewed by: Song Jiang
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 35C15
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35J47
Mathematics Subject Classification ID: 35J57
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 45M05
Mathematics Subject Classification ID: 47A50
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 47G40
Mathematics Subject Classification ID: 74A15
Mathematics Subject Classification ID: 74E30
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 74F15
Mathematics Subject Classification ID: 74G70
Mathematics Subject Classification ID: 74H35
zbMATH DE Number: 7887450
zbMATH Keywords: thermo-piezo-electricity without energy dissipation
zbMATH Keywords: Green-Naghdi's model
zbMATH Keywords: interface crack boundary-transmission problems
zbMATH Keywords: potential method
zbMATH Keywords: pseudodifferential equations
zbMATH Keywords: asymptotic properties of solutions
zbMATH Keywords: regularity of solutions
zbMATH Keywords: stress singularity exponents
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7887450