Measure-valued solutions of scalar hyperbolic conservation laws, Part 1: Existence and time evolution of singular parts

被引：0
|
作者：
Bertsch, Michiel [1 ,2 ]
Smarrazzo, Flavia [3 ]
Terracina, Andrea [4 ]
Tesei, Alberto [2 ,4 ]
机构：
[1] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Sci, I-00133 Rome, Italy
[2] CNR, Ist Applicazioni Calcolo M Picone, Rome, Italy
[3] Univ Campus Biomed Roma, Via Alvaro Portillo 21, I-00128 Rome, Italy
[4] Sapienza Univ Roma, Dipartimento Matemat G Castelnuovo, Ple A Moro 5, I-00185 Rome, Italy
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2024年 / 245卷
关键词：
First order hyperbolic conservation laws; Radon measure-valued entropy solutions; Continuity properties; Compatibility conditions; DELTA-SHOCK-WAVES; STRONG TRACES;
D O I：
10.1016/j.na.2024.113571
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页数：26
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