On the local and global behavior of weak shocks and induced discontinuities in a class of materials with internal state variables

We examine in this paper coupled governing differential equations of weak shocks and induced discontinuities in a class of materials with internal state variables, and under physically reasonable conditions deduce definite specific results concerning their local and global behavior. It is shown that all admissible choices of material parameters can be divided into four classes depending on their magnitudes, and the local and global behavior of shocks and induced discontinuities can have disparate features among the classes.