微伸缩的热弹性力学方程组柯西问题解的奇性传播

Propagation of Singularities of Solutions for Cauchy Problems of Thermoelastic Systems for Microstretch Materials

用频率分析对角化的方法,研究了一维线性微伸缩的热弹性力学方程组柯西问题解的奇性传播规律.首先从微局部观点出发,利用拟微分算子将双曲抛物的耦合方程组弱解耦.然后利用经典的双曲抛物方程理论和穿梭法,证明了柯西问题解的奇性传播具有有限传播速度、解的奇性沿双曲算子的零次特征带进行传播.

The propagation of singularities of solutions to the Cauchy problems of a linear thermoelastic system for microstretch materials in one space variable is studied by using an argument of frequencies analysis.Firstly,by using pseudodifferential operators,the coupled thermoelastic system for microstretch materials will be decoupled microlocally.Secondly, by using a classical bootstrap argument,the property of finite propagation speeds of singularities for the linear thermoelastic system is obtained.Finally,it is also shown that the microlocal weak singularities are propagated along the null bicharacteristics of the hyperbolic operators of the coupled system.