带第二声速的变系数热弹性力学方程组间断解的性态

主要研究一维空间变量的带第二声速的变系数线性及半线性热弹性力学方程Cauchy问题间断解的渐近性态.当松弛系数趋于零时,得到弹性体温度的间断将消失,弹性波和热流量的间断将以弹性波的速度传播;这些间断随时间增长呈指数衰减,且衰减率与非线性项的增长率、热传导系数、弹性波速度的变化率有关.

Asymptotic Behavior of Discontinuities in Thermoelasticity with Second Sound and Variable Coeffcients

This paper mainly studyied the asymptotic behavior of discontinuous solutions to the Cauchy problems for linear and semilinear thermoelastic equations with second sound and variable coefficients in one space variable. When the relaxation parameter goes to zero, the discontinuity of temperature vanishes, and discontinuities of elastic waves and heat flux are propagated with the elastic speeds. Moreover, these discontinuities decay exponentially when the time goes to infinity, and the decay rates not only depend on the growth rate of the nonlinear source terms and the heat conduction coefficient, but also depend on the change rates of the elastic speeds.