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
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10.1512/iumj.2006.55.2799
10.1512/iumj.2006.55.2799
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Indiana Univ. Math. J. 55 (2006) 1333 - 1362
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