Almost global existence of classical discontinuous solutions to genuinely nonlinear hyperbolic systems of conservation laws with small BV initial data
The author considers the Riemann solutions to a strictly hyperbolic and genuinely nonlinear system of conservation laws, which consist only of shock waves. The structural stability of these solutions under \(C^1\)-smooth perturbations of the Riemann data is studied. The author obtains the almost global existence and lifespan of piecewise \(C^1\)-smooth solutions of the perturbed problem. Applications to the system of one-dimensional isentropic flow are also given.
genuinely nonlinear characteristic fields
scientific article; zbMATH DE number 6147006