In this paper we investigate the propagation of discontinuity waves of order N > 1 through a homogeneous linear anisotropic thermo-viscoelastic solid whose heat flux vector depends upon the past history of the temperature gradient. We show that the normal speeds of propagation are independent of the order of the wave. Our analysis is simplified in the case of generalized longitudinal and transverse waves. For these waves we get also the evolution law of the discontinuities (which is the same for any N >= 1) along the rays associated with the wave front. © 1991.
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