On the physical indetermination of the response functions for general bodies of the differential tipe.

The paper is divided into two parts. The first part has a purely mathematical character and solves certain symmetric systems of linear partial differential equations with constant coefficients, which involve tensor-valued functions with tensor arguments. The results are further used in the second part in order to study the constitutive functions for a body BPQR of differential type, having the complexity (P, Q, R) (that is, the arguments of the constitutive functions iinclude the material time derivatives of the deformation gradient, temperature, and temperature gradient, where their possibly vanishing orders do not exceed P, Q and R respectively). Under the assumption of Galilean invariance, a uniqueness theorem is shown for the response function of the stress in BPQR for any (P, Q, R). Further, under the stronger assumption of Euclidean invariance, a uniqueness theorem is also proved for the response function of the internal energy in BP00, for any P. Generally, for any BPQR, a necessary and sufficient condition is stated for the difference between any two admissible response functions for the internal energy to be a function of the material point. It is shown that in case the aforementioned condition does not hold there is a threefold indetermination in the response functions for internal energy, entropy, and heat flux, which cannot be detected by experiments.