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Crowd dynamics through non-local conservation laws

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Abstract

We present a Lax-Friedrichs type scheme to compute the solutions of a class of non-local and non-linear systems of conservation laws in several space dimensions. The convergence of the approximate solutions is proved by providing suitable L 1, L ∞ and BV uniform bounds. To illustrate the performances of the scheme, we consider an application to crowd dynamics. Numerical integrations show the formation of lanes in groups moving in opposite directions. This is joint work with R.M. Colombo (INDAM Unit, University of Brescia).

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Author notes

  1. Aekta Aggarwal

    Present address: Indian Institute of Management Indore, Prabandh Shikhar, Rau-Pithampur Road, Indore, 453556, India

Authors and Affiliations

  1. INRIA Sophia Antipolis, Sophia Antipolis Cedex, France

    Aekta Aggarwal

  2. INRIA Sophia Antipolis – Méditerranée 2004, Route des Lucioles, BP 93, 06902, Sophia Antipolis Cedex, France

    Paola Goatin

Authors
  1. Aekta Aggarwal
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  2. Paola Goatin
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Correspondence to Aekta Aggarwal.

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Aggarwal, A., Goatin, P. Crowd dynamics through non-local conservation laws. Bull Braz Math Soc, New Series 47, 37–50 (2016). https://doi.org/10.1007/s00574-016-0120-7

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  • DOI: https://doi.org/10.1007/s00574-016-0120-7

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