Title: Well-posedness and decay estimates for Cauchy problems of linear thermoelastic systems of type III in 3-D

Authors: Lin Yang and Ya-Guang Wang

Issue: Volume 55 (2006), Issue 4, 1333-1362

Abstract: 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.