Small-Amplitude Discontinuities of Solutions to Equations of Continuum Mechanics

Abstract

A general approach is developed for problems of propagation of weak discontinuities against a known background for systems of hyperbolic equations that can be represented in a variational form. A weak shock wave is considered as an approximation to a solution containing a weak discontinuity. This method is applicable to the description of various adiabatic processes in continuum mechanics in the presence of variable force fields.