Regular solutions of first-order Hamilton-Jacobi equations for boundary control problems and applications to economics. (English) Zbl 1078.49026
The author presents an existence and uniqueness result for the (strong) solution of a Hamilton-Jacobi-Bellman equation related to a linear convex boundary control problem in a Hilbert space.
The (technically involved) proof is obtained via approximation of the equation by suitable families of auxiliary equations, the so-called mild equations and gradient equations. For these families of equations existence and uniqueness of classical solutions are established.
The (technically involved) proof is obtained via approximation of the equation by suitable families of auxiliary equations, the so-called mild equations and gradient equations. For these families of equations existence and uniqueness of classical solutions are established.
Reviewer: Lars Grüne (Bayreuth)
MSC:
| 49L20 | Dynamic programming in optimal control and differential games |
| 35B37 | PDE in connection with control problems (MSC2000) |
| 49L25 | Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games |
| 35F20 | Nonlinear first-order PDEs |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
