Nonuniqueness of unbounded solutions of the Cauchy problem for scalar conservation laws

DOI10.1007/S10958-019-04613-2zbMath1435.35007OpenAlexW2990794006WikidataQ114852343 ScholiaQ114852343MaRDI QIDQ2307726

L. V. Gargyants, Andrey Yu. Goritsky

Publication date: 25 March 2020

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-019-04613-2

zbMATH Keywords

quasilinear equationunbounded initial data

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Initial value problems for first-order hyperbolic equations (35L03)

Related Items (1)

Constructing unbounded discontinuous solutions of scalar conservation laws using the Legendre transform

Cites Work

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• Locally bounded solutions of one-dimensional conservation laws
• Example of nonuniqueness of entropy solutions in the class of locally bounded functions.
• Example of nonexistence of a positive generalized entropy solution of a Cauchy problem with unbounded positive initial data
• On locally bounded solutions of the Cauchy problem for a first-order quasilinear equation with power flux function

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