Sharp \(L^1\) stability estimates for hyperbolic conservation laws (Q5953292)

This paper deals with continuous dependence of entropy solutions to hyperbolic conservation laws where the flux is a smooth convex function, and aims at deriving sharp \(L^1\) estimates for general solution of bounded variation. Passing to the limit in wave front tracking approximations, the paper arrives at the sharp bound for general bounded variation solutions; the proof is based on convergence properties and on a technique of stability of nonconservative products developed earlier. Finally, the sharp \(L^1\) stability property is established for general bounded variation solutions using the technique of generalized characteristics. The paper may be of interest to someone interested on stability aspects for hyperbolic conservation laws.