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

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