Stability Conditions for Patterns of Noninteracting Large Shock Waves

In this paper we study different conditions whose presence is required for A. the admissibility and stability of large shocks present in solutions of a strictly hyperbolic n × n system of conservation laws in one space dimension ut + f(u)x = 0, B. the solvability and L well posedness of the Cauchy problem for the above equation, near solutions containing large and stable, but noninteracting shock waves. We compare the corresponding conditions of type A and B appearing in the literature; in particular, we show that the finiteness and stability conditions used in our most recent works generalize and/or unify these conditions in appropriate ways.