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  • 1
    Electronic Resource
    Electronic Resource
    A minimax problem for semilinear nonlocal competitive systems (1993)
    Springer
    Applied mathematics & optimization 28 (1993), S. 113-132 
    Details
    ISSN: 1432-0606
    Keywords: Elliptic systems ; Nonlinear competitive interactions ; Game theory ; Optimal control ; 49A45 ; 35K10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01182976
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  • 2
    Electronic Resource
    Electronic Resource
    Optimal control for parabolic systems with competitive interactions (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 509-524 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a two-dimensional parabolic system with general competitive interactions as a two-player game with conflicting objectives and with controls on the inhomogencous (source) terms. We show the existence of an optimal solution of the game as the saddle point of a suitable objective functional.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170703
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  • 3
    Electronic Resource
    Electronic Resource
    Transport equations with boundary conditions of reverse reflection type (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 15-35 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A study is performed of transport equations on arbitrary three-dimensional domains with boundary conditions of reverse reflection type. The existence of the dominant eigenvalue of the criticality problem is proved and its independence of the functional setting and its continuous dependence on a variety of data are established. The corresponding time-dependent problem is shown to be well-posed, also for a conservative boundary. The relationship between the criticality and the time-dependent problem is given explicitly.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100103
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