On the Cauchy problem for a one-dimensional conservation law with initial conditions coinciding with a power or exponential function at infinity

DOI10.1134/S001226612203003XzbMath1501.35254WikidataQ114075329 ScholiaQ114075329MaRDI QIDQ2671938

L. V. Gargyants

Publication date: 7 June 2022

Published in: Differential Equations (Search for Journal in Brave)

zbMATH Keywords

Legendre transformscalar conservation lawslocally bounded entropy solutionsOleinik's E-condition

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) Hyperbolic conservation laws (35L65) Initial value problems for first-order hyperbolic equations (35L03)

Cites Work

• Locally bounded solutions of one-dimensional conservation laws
• Construction of unbounded entropy solution of Cauchy problem with a countable number of shock waves
• Example of nonexistence of a positive generalized entropy solution of a Cauchy problem with unbounded positive initial data
• Conservation laws with continuous flux functions
• On locally bounded solutions of the Cauchy problem for a first-order quasilinear equation with power flux function
• On well-posedness classes of locally bounded generalized entropy solutions of the Cauchy problem for quasilinear first-order equations
• Constructing unbounded discontinuous solutions of scalar conservation laws using the Legendre transform
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
• A remark on the theory of generalized entropy sub- and supersolutions of the Cauchy problem for a first-order quasilinear equation
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