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Networks and Heterogeneous Media

2016, Volume 11, Issue 2: 331-348. doi: 10.3934/nhm.2016.11.331
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BV regularity near the interface for nonuniform convex discontinuous flux

  • 1.
    Gran Sasso Science Institute, Viale Francesco Crispi, 7, 67100 LAquila
  • Received: 01 April 2015 Revised: 01 September 2015

  • Primary: 35B65, 35L65, 35L67.

  • In this paper, we discuss the total variation bound for the solution of scalar conservation laws with discontinuous flux. We prove the smoothing effect of the equation forcing the BVloc solution near the interface for L∞ initial data without the assumption on the uniform convexity of the fluxes made as in [1,21]. The proof relies on the method of characteristics and the explicit formulas.

    Citation: Shyam Sundar Ghoshal. BV regularity near the interface for nonuniform convex discontinuous flux[J]. Networks and Heterogeneous Media, 2016, 11(2): 331-348. doi: 10.3934/nhm.2016.11.331

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    [2] Shyam Sundar Ghoshal, John D. Towers, Ganesh Vaidya . BV regularity of the adapted entropy solutions for conservation laws with infinitely many spatial discontinuities. Networks and Heterogeneous Media, 2024, 19(1): 196-213. doi: 10.3934/nhm.2024009
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  • In this paper, we discuss the total variation bound for the solution of scalar conservation laws with discontinuous flux. We prove the smoothing effect of the equation forcing the BVloc solution near the interface for L∞ initial data without the assumption on the uniform convexity of the fluxes made as in [1,21]. The proof relies on the method of characteristics and the explicit formulas.


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  • This article has been cited by:

    1. Shyam Sundar Ghoshal, John D. Towers, Ganesh Vaidya, A Godunov type scheme and error estimates for scalar conservation laws with Panov-type discontinuous flux, 2022, 151, 0029-599X, 601, 10.1007/s00211-022-01297-w
    2. Shyam Sundar Ghoshal, John D. Towers, Ganesh Vaidya, Convergence of a Godunov scheme for degenerate conservation laws with BV spatial flux and a study of Panov-type fluxes, 2022, 19, 0219-8916, 365, 10.1142/S0219891622500102
    3. Shyam Sundar Ghoshal, Animesh Jana, Nonexistence of the BV Regularizing Effect for Scalar Conservation Laws in Several Space Dimensions for C2 Fluxes, 2021, 53, 0036-1410, 1908, 10.1137/20M1371531
    4. Shyam Sundar Ghoshal, Animesh Jana, John D. Towers, Convergence of a Godunov scheme to an Audusse–Perthame adapted entropy solution for conservation laws with BV spatial flux, 2020, 146, 0029-599X, 629, 10.1007/s00211-020-01150-y
    5. Shyam Sundar Ghoshal, Stéphane Junca, Akash Parmar, Fractional regularity for conservation laws with discontinuous flux, 2024, 75, 14681218, 103960, 10.1016/j.nonrwa.2023.103960
    6. Shyam Sundar Ghoshal, John D. Towers, Ganesh Vaidya, BV regularity of the adapted entropy solutions for conservation laws with infinitely many spatial discontinuities, 2024, 19, 1556-1801, 196, 10.3934/nhm.2024009
    7. S. S. Ghoshal, S. Junca, A. Parmar, Higher Regularity for Entropy Solutions of Conservation Laws with Geometrically Constrained Discontinuous Flux, 2024, 56, 0036-1410, 6121, 10.1137/23M1604199
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