THE EQUATIONS OF ELASTICITY WITH DISSIPATION AS A NONTRIVIAL EXAMPLE OF THERMODYNAMICALLY CONSISTENT HYPERBOLIC EQUATIONS

A thermodynamically consistent Galilean-invariant formalization of the elasticity equations is proposed. The equations under consideration form a symmetric hyperbolic system but they are non-conservative. The conservation laws are valid only on a solution with special initial values. Difficulties arising while introducing the dissipative terms are briefly discussed.