非均匀材料耦合热弹性问题解的存在唯一性

Existence for the Classical Therm-elastic Problem of Nonhomogeneous Media

考虑非均匀材料耦合热弹性问题,此问题中含有关于瞬态位移场的动态热弹性方程和关于瞬态温度场的动态热传导方程,在求解时需考虑动态强耦合的温度场和位移场.本文基于热弹性本构方程建立了描述均匀材料热弹性行为的相关模型,并利用Fadeo-Galerkin方法,证明了非均匀介质耦合热弹性问题弱解的存在唯一性.

The paper studies classical therm-elastic model for nonhomogeneous media that consists of a system of dynamic thermoelasticity equations of displacement and dynamic heat conduction equation. This system is a coupled dynamic problem and the displacement and heat field must be solved at the same time. By using Fadeo-Galerkin method, we prove that there exists unique weak solution for the problem we proposed under some regular assumption.