Existence, uniqueness and regularity of the solution of the first boundary-initial value problem for the equations of linear thermo- microelasticity
type: Item
instance of: scholarly article
title: Existence, uniqueness and regularity of the solution of the first boundary-initial value problem for the equations of linear thermo- microelasticity
zbMATH Open document ID: 0621.73004
published in: Bulletin of the Polish Academy of Sciences. Technical Sciences
publication date: 1986-01-01T00:00:00Z
review text: Existence, uniqueness and regularity theorems for an initial-boundary value problem of linear homogeneous isotropic micropolar thermoelasticity are proved by using a method of Faedo-Galerkin type. A weak solution to the problem is shown to exist in a Sobolev space provided the data belong to suitable functional spaces. To show existence of a classical solution using an embedding theorem, rather stringent conditions on the data are imposed. The reviewer notes a number of misprints: e.g. 1. Two of the eight inequalities involving material constants on page 448 are superfluous. 2. In the definition (2.9) \(t\in X\) should read \(t\in I\).
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 35A15
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74G30
Mathematics Subject Classification ID: 74H25
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 4007784
zbMATH Keywords: Existence
zbMATH Keywords: regularity
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: linear homogeneous isotropic micropolar thermoelasticity
zbMATH Keywords: method of Faedo-Galerkin type
zbMATH Keywords: weak solution
zbMATH Keywords: Sobolev space
zbMATH Keywords: embedding theorem
author: Jerzy August Gawinecki
reviewed by: Józef Ignaczak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4007784