A minimax problem for semilinear nonlocal competitive systems |
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| Authors: | S Lenhart V Protopopescu S Stojanovic |
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| Institution: | (1) Mathematics Department, University of Tennessee, 37996 Knoxville, TN, USA;(2) Engineering Physics and Mathematics Division, Oak Ridge National Laboratory, 37831-6363 Oak Ridge, TN, USA;(3) Department of Mathematical Sciences, University of Cincinnati, 45221 Cincinnati, OH, USA |
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| Abstract: | A two-sided game for the control of a stationary semilinear competitive system with autonomous sources is considered, where the controls are the kernels of the nonlocal interaction terms. The saddle point (the optimal solution of the game) is characterized as the unique solution of the associated optimality system, which is solved by an iterative scheme.This research has been partially sponsored by DARPA under Contract No. 1868-A037-A1 with Martin Marietta Energy Systems, Inc., under Contract No. DE-AC05-84OR21400 with U.S. Department of Energy. S. Lenhart's work was also partially supported by an NSF grant. |
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| Keywords: | Elliptic systems Nonlinear competitive interactions Game theory Optimal control |
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