Applied Mathematical Modelling
Partial differential equations -- Hyperbolic equations and systems -- Nonlinear first-order hyperbolic equations
The method of singular surfaces is used to obtain explicit conditions under which a one-dimensional acceleration wave develops into a shock when some dissipation mechanism is present. The conditions which secure the initial growth of the strong shock wave propagating into an undeformed nonlinear and dissipative medium are also derived. The analysis is pre- sented for a single balance law, one-dimensional elasticity, and the non- linear Maxwellian continuum.
Elżanowski, M., & Epstein, M. (1988). The decay and formation of one-dimensional nonconservative shocks. Applied mathematical modelling, 12(3), 280-284.