Well-posedness and decay estimates for Cauchy problems of linear thermoelastic systems of type III in 3-D Ya-Guang WangLiming Yang 35Q3035A2180A17L^p-L^q decay estimatespropagation of singularitiesCauchy problemsthermoelasticity of type III The well-posedness, $L^p$--$L^q$ decay estimates and propagation of singularities of solutions to the Cauchy problems of linear thermoelastic systems of type III in three space variables are studied. Firstly, the thermoelastic system is transformed into an equivalent one of first order in $t$ by some special transformations. Secondly, we obtain the asymptotic behaviors of characteristic roots of the system for higher, middle, and lower frequencies, respectively, by using a diagonalization argument. From the behaviors of characteristic roots and the diagonalization procedure, we conclude the well-posedness, $L^p$--$L^q$ decay estimates, and the propagation of singularities of solutions to the Cauchy problem. Indiana University Mathematics Journal 2006 text pdf 10.1512/iumj.2006.55.2799 10.1512/iumj.2006.55.2799 en Indiana Univ. Math. J. 55 (2006) 1333 - 1362 state-of-the-art mathematics http://iumj.org/access/