Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

Plaksin, A. R.
Differential Equations , Volume 57 (11) – Nov 1, 2021
Download PDF
11 pages

Loading next page...
 
/lp/springer-journals/on-the-minimax-solution-of-the-hamilton-jacobi-equations-for-neutral-t8N0F56iQF
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 Equations – Springer Journals

Published: Nov 1, 2021

References

  • The Hamilton–Jacobi equation for hereditary systems: minimax and viscosity solutions
    Lukoyanov, N.Yu.
  • On the Hamilton–Jacobi–Isaacs–Bellman equation for systems of neutral type
    Plaksin, A.R.
  • Minimax solution of functional Hamilton–Jacobi equations for neutral type systems
    Plaksin, A.R.
  • Hamilton–Jacobi equations for neutral-type systems: inequalities for directional derivatives of minimax solutions
    Lukoyanov, N.Yu.; Plaksin, A.R.
  • Differential games of systems with aftereffect
    Osipov, Yu.S.
  • On basic equation of differential games for neutral-type systems
    Gomoyunov, M.I.; Plaksin, A.R.
  • On the theory of positional differential games for systems of neutral type
    Lukoyanov, N.Yu.; Plaksin, A.R.
  • Existence, uniqueness and continuous dependence for hereditary systems
    Hale, J.K.; Cruz, M.A.