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Quasi-static limit for a hyperbolic conservation law

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Abstract

We study the quasi-static limit for the \(L^\infty \) entropy weak solution of scalar one-dimensional hyperbolic equations with strictly concave or convex flux and time dependent boundary conditions. The quasi-stationary profile evolves with the quasi-static equation, whose entropy solution is determined by the stationary profile corresponding to the boundary data at a given time.

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Authors and Affiliations

  1. GSSI, 67100, L’Aquila, Italy

    Stefano Marchesani, Stefano Olla & Lu Xu

  2. CEREMADE, UMR CNRS Université Paris-Dauphine, PSL Research University, 75016, Paris, France

    Stefano Olla

Authors
  1. Stefano Marchesani
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  2. Stefano Olla
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  3. Lu Xu
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Correspondence to Stefano Olla.

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This work was partially supported by ANR-15-CE40-0020-01 grant LSD. We thank Anna De Masi for inspiring discussions and remarks. We thank an anonimous referee whose comments and suggestions helped improve our results and presentation.

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Marchesani, S., Olla, S. & Xu, L. Quasi-static limit for a hyperbolic conservation law. Nonlinear Differ. Equ. Appl. 28, 53 (2021). https://doi.org/10.1007/s00030-021-00716-5

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  • DOI: https://doi.org/10.1007/s00030-021-00716-5

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