Microlocal analysis in nonlinear thermoelasticity Original Research Article

This paper is devoted to the study of the propagation of singularities for semilinear hyperbolic–parabolic coupled systems in thermoelasticity. First, a linear transformation involving pseudodifferential operators for unknowns is introduced to decouple the hyperbolic and the parabolic operators. By using the decoupled system, we obtain that the semilinear system of thermoelasticity has finite speeds for the propagation of singularities. Furthermore, it is proved that the microlocal singularities of solutions to this semilinear hyperbolic–parabolic coupled system are propagated along null bicharacteristics of the hyperbolic operator by using the theory of nonsmooth pseudodifferential operators. Finally, the Cauchy problem for the semilinear system of thermoelasticity is investigated when the initial data have singularities.