We investigate the long time behaviour of the $L^2$-energy of solutions to wave equations with variable speed. The novelty of the approach is the combination of estimates for higher order derivatives of the coefficient with a stabilisation property.
In this note we develop tools and techniques for the treatment of anisotropic thermo-elasticity in two space dimensions. We use a diagonalisation technique to obtain properties of the characteristic roots of the full symbol of the system in order to prove $L^p$--$L^q$ decay rates for its solutions.
