Abstract
We consider a two-dimensional parabolic system with general competitive interactions as a two-player game with conflicting objectives. The controls are on the initial conditions. We demonstrate the existence of an optimal solution of the game as the saddle point for a suitably defined objective functional. The saddle point is the solution to an optimality system solved by a constructive convergence scheme.
| Original language | English |
|---|---|
| Pages (from-to) | 215-245 |
| Number of pages | 31 |
| Journal | Applied Mathematics and Computation |
| Volume | 59 |
| Issue number | 2-3 |
| DOIs | |
| State | Published - Dec 1993 |
Funding
*This research was partly supported by the U.S. Department of Energy under contract number DE-AC05-840R21400 with Martin Marietta Energy Systems, Inc. Adam Szpiro’s contribution to this paper is part of his activity as a participant in the Science and Engineering Research Semester sponsored by ORAU. The authors thank Ms. Carolyn Householder for help in preparing this manuscript and Dr. Suzanne Lenhart for her useful comments. “The submitted manuscript has been authored by a contractor of the U.S. Government under contract No. DE-AC05-840R21400. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so. for U.S. Government purposes.”