Discontinuous Solutions of Hamilton-Jacobi Equations Versus Radon Measure-Valued Solutions of Scalar Conservation Laws: Disappearance of Singularities

被引：2

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, 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：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2023年 / 35卷 / 01期

关键词：

Hamilton-Jacobi equation; First order hyperbolic conservation laws; Singular boundary conditions; Waiting time; SEMICONTINUOUS VISCOSITY SOLUTIONS; UNIQUENESS;

D O I：

10.1007/s10884-021-09997-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let H be a bounded and Lipschitz continuous function. We consider discontinuous viscosity solutions of the Hamilton-Jacobi equation U-t + H(U-x) = 0 and signed Radon measure valued entropy solutions of the conservation law u(t) + [H(u)](x) = 0. After having proved a precise statement of the formal relation U-x = u, we establish estimates for the (strictly positive!) times at which singularities of the solutions disappear. Here singularities are jump discontinuities in case of the Hamilton-Jacobi equation and signed singular measures in case of the conservation law.

引用

页码：455 / 491

页数：37

共 50 条

[21] Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients
Coclite, Giuseppe Maria
Risebro, Nils Henrik
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2007, 4 (04) : 771 - 795
[22] MEASURE-VALUED SOLUTIONS OF SCALAR CONSERVATION-LAWS WITH BOUNDARY-CONDITIONS
SZEPESSY, A
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1989, 107 (02) : 181 - 193
[23] Solutions to switched Hamilton-Jacobi equations and conservation laws using hybrid components
Claudel, Christian G.
Bayen, Alexandre M.
HYBRID SYSTEMS: COMPUTATION AND CONTROL, 2008, 4981 : 101 - 115
[24] RADON MEASURE-VALUED SOLUTIONS OF UNSTEADY FILTRATION EQUATIONS
Porzio, Maria Michaela
Smarrazzo, Flavia
Tesei, Alberto
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2022, : 1595 - 1624
[25] Radon measure-valued solutions of quasilinear parabolic equations
Tesei, Alberto
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2021, 32 (02) : 213 - 231
[26] Dissipative measure-valued solutions for general conservation laws
Gwiazda, Piotr
Kreml, Ondrej
Swierczewska-Gwiazda, Agnieszka
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2020, 37 (03): : 683 - 707
[27] A simple proof of the propagation of singularities for solutions of Hamilton-Jacobi equations
Yu, Yifeng
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2006, 5 (04) : 439 - 444
[28] Boundary singularities of positive solutions of quasilinear Hamilton-Jacobi equations
Bidaut-Veron, Marie-Francoise
Garcia-Huidobro, Marta
Veron, Laurent
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (04) : 3471 - 3515
[29] Boundary singularities of solutions to elliptic viscous Hamilton-Jacobi equations
Tai Nguyen Phuoc
Veron, Laurent
JOURNAL OF FUNCTIONAL ANALYSIS, 2012, 263 (06) : 1487 - 1538
[30] Discontinuous solutions of Hamilton-Jacobi equations: Existence, uniqueness, and regularity
Chen, GQ
Su, B
HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS, 2003, : 443 - 453

← 1 2 3 4 5 →