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

Abstract

The well-posedness,L p -L q decay estimates and prop- agation 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 transforma- tions. Secondly, we obtain the asymptotic behaviors of character- istic roots of the system for higher, middle, and lower frequencies, respectively, by using a diagonalization argument. From the be- haviors 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.