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.
Measure-valued solutions of scalar hyperbolic conservation laws, Part 1: Existence and time evolution of singular parts / Bertsch, Michiel; Smarrazzo, Flavia; Terracina, Andrea; Tesei, Alberto. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - 245:(2024). [10.1016/j.na.2024.113571]
Measure-valued solutions of scalar hyperbolic conservation laws, Part 1: Existence and time evolution of singular parts
Terracina, Andrea;Tesei, Alberto
2024
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.