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A Viscosity Solution Approach to the Infinite-Dimensional HJB Equation Related to a Boundary Control Problem in a Transport Equation

Author

Listed:
  • Giorgio Fabbri

    (LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

Abstract

The paper concerns the infinite-dimensional Hamilton–Jacobi–Bellman equation related to an optimal control problem regulated by a linear transport equation with boundary control. A suitable viscosity solution approach is needed in view of the presence of the unbounded control-related term in the state equation in the Hilbert setting. An existence-and-uniqueness result is obtained.

Suggested Citation

  • Giorgio Fabbri, 2008. "A Viscosity Solution Approach to the Infinite-Dimensional HJB Equation Related to a Boundary Control Problem in a Transport Equation," Post-Print hal-01615450, HAL.
    • Handle: RePEc:hal:journl:hal-01615450
    DOI: 10.1137/050638813
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    Cited by:

    1. Fabbri, Giorgio, 2006. "Viscosity solutions approach to economic models governed by DDEs," MPRA Paper 2826, University Library of Munich, Germany.
    2. Ballestra, Luca Vincenzo, 2016. "The spatial AK model and the Pontryagin maximum principle," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 87-94.
    3. Silvia Faggian, 2008. "Equilibrium Points for Optimal Investment with Vintage Capital," Working Papers 182, Department of Applied Mathematics, Università Ca' Foscari Venezia.

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