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In contrast to conventional explosives which constitute rapid decomposition of the molecular structure acconlpanied by the release of large volumes of gaseous products, heterogeneous mixtures in the SHS realm react by progression of a thermal wave at velocities far below the speed of sound in such mixtures. Interestingly, ultrafast solid phase reactions can be initiated under the right conditions. A shock wave compresses the solid mixture to densities well beyond the theoretical mean ambient density (TMD) and compression becomes the major form of preheating. In addition, elastic potential energy is pumped into the lattice structure to induce severe distortion and eventually a structural collapse of the lattice on the atomic scale. Mixing and reaction proceed as in a dense gas and condensed products form. A continuum model is presented which addresses the following elements in the process. Compaction of the porous preform is described by an amended equation of state which includes plastic yielding and dilatation. The equation of state of densified material is based on an isobaric modification of the Mie-Gruneisen equation of state to account for anomalous behavior - a phenomenon of density reduction in the shock wave. Pressure is coupled into the kinetics as suggested by Benderskii insofar the activation energy is reduced proportionally to the stored elastic potential energy. Examples are presented of anomalous shock behavior, stable and unstable detonations.