Sonya Kovalevsky, in the celebrated Cauchy-Kovalevsky theorem, made clear the significance of characteristics in partial differential equations. In the field of hyperbolic conservation laws, characteristic curves (in one space dimension) and surfaces (in higher dimensions) dominate the behavior of solutions. Some examples of systems exhibit interesting, one might even say pathological, characteristic behavior. This talk will focus on ways that characteristics in systems of conservation laws give information about the systems being modeled.
