On shock waves and phase-transition fronts in continua

Abstract

The canonical formalism that considers simultaneously the second law of thermodynamics and the balance of canonical momentum is used to incorporate the case of shock waves among those singularity sets whose dissipation is in fact related to the power expanded by a driving force — a force on the material manifold and not in physical space — in an irreversible motion of the singularity set. A relationship between this and the presence of a generally non-zero quasi-inhomogeneity material force at the wave front is established. Extensions to electromagnetic continua of various types are given and the case of shock waves is thoroughly compared to that of phase-transition fronts in the same continua. The relationship with solitonic and moving localized dissipative structures is enunciated.