Abstract
We study a Hamilton-Jacobi equation in infinite dimensions arising in optimal control theory for problems involving both exit times and state-space constraints. The corresponding boundary conditions for the Hamilton-Jacobi equation, of mixed nature, have been derived and investigated in [19], [2], [5], and [15] in the finite-dimensional case. We obtain a uniqueness result for viscosity solutions of such a problem and then prove the existence of a solution by showing that the value function is continuous.
Original language | English (US) |
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Pages (from-to) | 197-220 |
Number of pages | 24 |
Journal | Applied Mathematics & Optimization |
Volume | 24 |
Issue number | 1 |
DOIs | |
State | Published - Jul 1991 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Applied Mathematics