Abstract
In this chapter we study the Cauchy problems for one-dimensional scalar conservation laws. In particular, we prove that the Cauchy problem is well posed in the class of entropy weak solutions, in the sense that it admits a unique entropy weak solution. The existence of the solutions is proved by the method of wave front tracking. The uniqueness is proved by showing the Kružkov result of the L1 contractiveness of the flow generated by a scalar conservation law.
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Rosini, M.D. (2013). The Cauchy Problem. In: Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications. Understanding Complex Systems. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00155-5_5
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DOI: https://doi.org/10.1007/978-3-319-00155-5_5
Publisher Name: Springer, Heidelberg
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