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Viscosity Solutions of Hamilton–Jacobi Equations for Neutral-Type Systems

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Abstract

The paper deals with path-dependent Hamilton–Jacobi equations with a coinvariant derivative which arise in investigations of optimal control problems and differential games for neutral-type systems in Hale’s form. A viscosity (generalized) solution of a Cauchy problem for such equations is considered. The existence, uniqueness, and consistency of the viscosity solution are proved. Equivalent definitions of the viscosity solution, including the definitions of minimax and Dini solutions, are obtained. Application of the results to an optimal control problem for neutral-type systems in Hale’s form are given.

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Funding

Funding was provided by Grant of the RSF No. 21-71-10070.

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Authors and Affiliations

  1. N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str, Yekaterinburg, Russia, 620108

    Anton Plaksin

  2. Ural Federal University, 19 Mira street, Yekaterinburg, Russia, 620002

    Anton Plaksin

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Plaksin, A. Viscosity Solutions of Hamilton–Jacobi Equations for Neutral-Type Systems. Appl Math Optim 88, 6 (2023). https://doi.org/10.1007/s00245-023-09980-6

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