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A well posed conservation law with a variable unilateral constraint. (English) Zbl 1116.35087
Summary: This paper considers the Cauchy problem for a conservation law with a variable unilateral constraint, its motivation being, for instance, the modeling of a toll gate along a highway. This problem is solved by means of nonclassical shocks and its well posedness is proved. Then, the solutions so obtained are shown to coincide with the limits of the classical solutions to suitable conservation laws with discontinuous flux function that approximate the constrained problem.

35L65 Hyperbolic conservation laws
90B20 Traffic problems in operations research
35L45 Initial value problems for first-order hyperbolic systems
35L67 Shocks and singularities for hyperbolic equations
Full Text: DOI
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