Viscosity solutions of first-order Hamilton-Jacobi equations and applications. (Solutions de viscosité des équations de Hamilton-Jacobi du premier ordre et applications.) (French) Zbl 0595.35023

Lions, Pierre-Louis

Sémin. Goulaouic-Meyer-Schwartz 1983-1984, Équat. dériv. part., Exp. No. 6, 12 p. (1984).

This article is a survey of some resent results involving viscosity solutions of first-order Hamilton-Jacobi equations. The definition and elementary properties are given. Existence and uniqueness results and applications to deterministic optimal control are discussed. A section is devoted to some asymptotic problems for H-J equations.

Reviewer: S. Lenhart (Knoxville)

MSC:

35F21	Hamilton-Jacobi equations
35-02	Research exposition (monographs, survey articles) pertaining to partial differential equations
49L25	Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games

Keywords:

survey; viscosity solutions; first order Hamilton-Jacobi equations; existence; uniqueness; deterministic optimal control; asymptotic problems