We prove existence for a class of signed Radon measure-valued entropy solutions of the Cauchy problem for a first order scalar hyperbolic conservation law in one space dimension. The initial data of the problem is a finite superposition of Dirac masses, whereas the flux is Lipschitz continuous. Existence is proven by a constructive procedure which makes use of a suitable family of approximating problems. Relevant qualitative properties of such constructed solutions are pointed out.
Bertsch, M., Smarrazzo, F., Terracina, A., Tesei, A. (2024). Measure-valued solutions of scalar hyperbolic conservation laws, Part 1: Existence and time evolution of singular parts. NONLINEAR ANALYSIS, 245 [10.1016/j.na.2024.113571].
Measure-valued solutions of scalar hyperbolic conservation laws, Part 1: Existence and time evolution of singular parts
Bertsch M.;
2024-01-01
Abstract
We prove existence for a class of signed Radon measure-valued entropy solutions of the Cauchy problem for a first order scalar hyperbolic conservation law in one space dimension. The initial data of the problem is a finite superposition of Dirac masses, whereas the flux is Lipschitz continuous. Existence is proven by a constructive procedure which makes use of a suitable family of approximating problems. Relevant qualitative properties of such constructed solutions are pointed out.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
