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On the Minimax Solution of the Hamilton-Jacobi Equations for Neutral-Type Systems: the Case of an Inhomogeneous Hamiltonian

On the Minimax Solution of the Hamilton-Jacobi Equations for Neutral-Type Systems: the Case of an... We study the Hamilton–Jacobi equation with coinvariant derivatives corresponding todynamical systems of the neutral type. Moreover, in contrast to the previous papers, theHamiltonian in the equation may not satisfy the homogeneity condition. We give a definition ofa minimax (generalized) solution of this equation. The existence and uniqueness of this solution isproved, and its consistency with the concept of solution in the classical sense is established. Theproofs are based on the choice of a suitable Lyapunov–Krasovskii functional. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On the Minimax Solution of the Hamilton-Jacobi Equations for Neutral-Type Systems: the Case of an Inhomogeneous Hamiltonian

Differential Equations , Volume 57 (11) – Nov 1, 2021

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Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2021
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/s0012266121110100
Publisher site
See Article on Publisher Site

Abstract

We study the Hamilton–Jacobi equation with coinvariant derivatives corresponding todynamical systems of the neutral type. Moreover, in contrast to the previous papers, theHamiltonian in the equation may not satisfy the homogeneity condition. We give a definition ofa minimax (generalized) solution of this equation. The existence and uniqueness of this solution isproved, and its consistency with the concept of solution in the classical sense is established. Theproofs are based on the choice of a suitable Lyapunov–Krasovskii functional.

Journal

Differential EquationsSpringer Journals

Published: Nov 1, 2021

References