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

Smarrazzo, Flavia;
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.
2024
First order hyperbolic conservation laws; Radon measure-valued entropy solutions; Continuity properties; Compatibility conditions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12610/78725
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