Well-posedness of the Cauchy problem for nxn systems of conservation laws (original) (raw)

The paper investigates the well-posedness of the Cauchy problem for n × n strictly hyperbolic systems of conservation laws in one dimension, focusing on uniqueness and continuous dependence of weak solutions on initial conditions. Building on Glimm's theorem, it establishes conditions under which solutions remain Lipschitz continuous in L1 norm with respect to initial data, encompasses the existence of a Standard Riemann Semigroup, and articulates key estimates vital for analysis. Notably, the paper contributes a generalized theorem for broader classes of systems while addressing implications for numerical schemes and solution behaviors.