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$$L^p-L^q$$-estimates for solutions to the equations of linear thermoelasticity in exterior domains. (English) Zbl 0724.35019
The author studies local decay, $$L^p-L^q$$ decay, and decay estimates for derivatives for solutions (of the “coupled part”) of the linear equations of thermoelasticity in the exterior of a star shaped domain. One of the main ingredients is the use of generalized Fourier transforms (i.e. of generalized eigenfunction expansions) associated with the Laplace operator with Dirichlet boundary conditions.

##### MSC:
 35B40 Asymptotic behavior of solutions to PDEs 35M20 PDE of composite type (MSC2000) 74B99 Elastic materials 42C15 General harmonic expansions, frames
##### Keywords:
decay estimates; thermoelasticity