On plane displacement boundary value problem of quasi–static linear thermoelasticity

Abstract

The displacement boundary value problem of qusi–static linear thermoe–lasticity is considered. The results of Previous literature (shi and Xu⁵) are improved by more accurate estimation. By a careful investigation of a certain integral operator and by utilizing of Green's function and Bergman kernel of the domain, the thermoelastic systems on bounded simply-connected domain Ω is decoupled. The decoupled temperature equation is studied by using the contractive mappling principle. Representation of solution of the field equation is obtained, and some solvability results are proved.

Keywords:

• thermoelasticity
• displacement boundary value problem
• decoupling
• function theoretic methods
• Bergman kernel of the domain
• contractive mapping principle

AMS:

• 35K50
• 73C03
• 73C25