A variational calculus for discontinuous solutions of systems of conservation laws (original) (raw)

This paper addresses the Cauchy problem for perturbed systems of conservation laws in one space variable, focusing on piecewise Lipschitz continuous solutions. It develops a variational calculus framework for analyzing first-order variations of these solutions by introducing generalized tangent vectors and exploring their evolution over time. Results indicate that under certain conditions, the problem admits solutions that depend continuously on initial data and allow the study of discontinuities and interactions in the solution. Practical implications of this work include insights into the behavior of systems exhibiting discontinuous solutions, which are prevalent in various applications of fluid dynamics and traffic flow.