### Saturday, May 9

## MS20

Representations of Solutions to Hamilton-Jacobi Equations

10:30 AM-12:30 PM

*Jacksonville A&B*

The speakers in this minisymposium will focus on explicitly finding or representing the solution to a Hamilton-Jacobi equation arising in deterministic optimal control theory. Two approaches will be discussed: (1) an explicit solution technique based on solving a free boundary problem, and (2) generalizations of the Hopf-Lax envelope representation formula. The problem formulations for these results necessarily require some special structure which, however, cover many important applications.

**Organizer: Peter R. Wolenski**

*Louisiana State University*

**10:30 The Converse Lyapunov Theorem and Viscosity Solutions**
*E. N. Barron* and R. Jensen, Loyola University, Chicago
**11:00 Envelope Representations of Value Functions**
*R. Tyrrell Rockafellar*, University of Washington; and Peter R. Wolenski, Organizer
**11:30 Smooth and Nonsmooth Fit for the Value Function of a Convex Control Problem**
*Guillermo Ferreyra* and J. R. Dorroh, Louisiana State University
**12:00 Duality in Fully Convex Control Problems**
- Peter R. Wolenski, Organizer

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*MMD, 5/5/98*