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Networks and Heterogeneous Media

2013, Volume 8, Issue 3: 707-726. doi: 10.3934/nhm.2013.8.707
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Viability approach to Hamilton-Jacobi-Moskowitz problem involving variable regulation parameters

  • 1.
    ENSTA ParisTech, 828, Boulevard des Maréchaux, 91762 Palaiseau Cedex
  • Received: 01 April 2012 Revised: 01 July 2013

  • Primary: 49J40, 34A60; Secondary: 35L65.

  • A few applications of the viability theory to the solution to the Hamilton-Jacobi-Moskowitz problems are presented. In the considered problem the Hamiltonian (fundamental diagram) depends on time, position and/or some regulation parameters. We study such a problem in its equivalent variational formulation. In this case, the corresponding lagrangian depends on the state of the characteristic dynamical system. As the Lax-Hopf formulae that give the solution in a semi-explicit form for an homogeneous lagrangian do not hold, a capture basin algorithm is proposed to compute the Moskowitz function as a viability solution of the Hamilton-Jacobi-Moskowitz problem with general conditions (including initial, boundary and internal conditions). We present two examples of applications to traffic regulation problems.

    Citation: Anya Désilles. Viability approach to Hamilton-Jacobi-Moskowitz problem involving variable regulation parameters[J]. Networks and Heterogeneous Media, 2013, 8(3): 707-726. doi: 10.3934/nhm.2013.8.707

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  • A few applications of the viability theory to the solution to the Hamilton-Jacobi-Moskowitz problems are presented. In the considered problem the Hamiltonian (fundamental diagram) depends on time, position and/or some regulation parameters. We study such a problem in its equivalent variational formulation. In this case, the corresponding lagrangian depends on the state of the characteristic dynamical system. As the Lax-Hopf formulae that give the solution in a semi-explicit form for an homogeneous lagrangian do not hold, a capture basin algorithm is proposed to compute the Moskowitz function as a viability solution of the Hamilton-Jacobi-Moskowitz problem with general conditions (including initial, boundary and internal conditions). We present two examples of applications to traffic regulation problems.


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  • This article has been cited by:

    1. Jean-Pierre Aubin, Chen Luxi, Anya Désilles, Cournot Maps for Intercepting Evader Evolutions by a Pursuer, 2015, 5, 2153-0785, 275, 10.1007/s13235-014-0133-z
    2. Jean-Pierre Aubin, Luxi Chen, 2015, Chapter 1, 978-3-319-06916-6, 1, 10.1007/978-3-319-06917-3_1
    3. Jean-Pierre Aubin, Regulation of Viable and Optimal Cohorts, 2015, 72, 0095-4616, 203, 10.1007/s00245-014-9277-x
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