SIGNED RADON MEASURE-VALUED SOLUTIONS OF FLUX SATURATED SCALAR CONSERVATION LAWS

被引：5

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 Applicaz Calcolo M Picone, Rome, Italy

[3] Univ Campus Biomed Roma, Fac Dipartimentale Ingn, Via Alvaro del Portillo 21, I-00128 Rome, Italy

[4] Univ Sapienza Roma, Dipartimento Matemat G Castelnuovo, Ple A Moro 5, I-00185 Rome, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2020年 / 40卷 / 06期

关键词：

First order hyperbolic conservation laws; signed Radon measures; singular boundary conditions; entropy inequalities; uniqueness;

D O I：

10.3934/dcds.2020041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove existence and uniqueness 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 and bounded. The solution class is determined by an additional condition which is needed to prove uniqueness.

引用

页码：3143 / 3169

页数：27

共 50 条

[31] Strong traces for solutions to scalar conservation laws with general flux
Kwon, Young-Sam
Vasseur, Alexis
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2007, 185 (03) : 495 - 513
[32] Mild solutions to a measure-valued mass evolution problem with flux boundary conditions
Evers, Joep H. M.
Hille, Sander C.
Muntean, Adrian
JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (03) : 1068 - 1097
[33] Existence and asymptotic behavior of Radon measure-valued solutions for a class of nonlinear parabolic equations
Quincy Stévène Nkombo
Fengquan Li
Christian Tathy
Advances in Difference Equations, 2021
[34] Measure valued solutions to conservation laws motivated by traffic modelling
Benzoni-Gavage, Sylvie
Colombo, Rinaldo M.
Gwiazda, Piotr
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2006, 462 (2070): : 1791 - 1803
[35] Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow
Bonicatto, Paolo
Gusev, Nikolay A.
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2019, 30 (03) : 511 - 531
[36] Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow
Bonicatto P.
Gusev N.A.
Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni, 2019, 30 (03): : 511 - 531
[37] Measure-valued solutions for models of ferroelectric materials
Kraynyukova, Nataliya
Nesenenko, Sergiy
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2014, 144 (05) : 935 - 963
[38] Measure-valued solutions to the complete Euler system
Brezina, Jan
Feireisl, Eduard
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2018, 70 (04) : 1227 - 1245
[39] Solutions to scalar conservation laws where the flux is discontinuous in space and time
Ostrov, DN
HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS, VOLS I AND II, 2001, 140 : 785 - 790
[40] STRUCTURE OF ENTROPY SOLUTIONS TO SCALAR CONSERVATION LAWS WITH STRICTLY CONVEX FLUX
Adimurthi
Ghoshal, Shyam Sundar
Gowda, G. D. Veerappa
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2012, 9 (04) : 571 - 611

← 1 2 3 4 5 →