关键词: 双曲, 热弹性力学方程组, 线性和半线性, Cauchy问题, 变系数, 渐近性态

Abstract: 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.