Uniqueness of the optimal control for a Lotka-Volterra control problem with a large crowding effect

J. L. Gámez; J. A. Montero

ESAIM: Control, Optimisation and Calculus of Variations (1997)

  • Volume: 2, page 1-12
  • ISSN: 1292-8119

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Gámez, J. L., and Montero, J. A.. "Uniqueness of the optimal control for a Lotka-Volterra control problem with a large crowding effect." ESAIM: Control, Optimisation and Calculus of Variations 2 (1997): 1-12. <http://eudml.org/doc/90506>.

@article{Gámez1997,
author = {Gámez, J. L., Montero, J. A.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {admissible control; iterative approximation; optimal control; partial differential equation of Lotka-Volterra type; optimality system},
language = {eng},
pages = {1-12},
publisher = {EDP Sciences},
title = {Uniqueness of the optimal control for a Lotka-Volterra control problem with a large crowding effect},
url = {http://eudml.org/doc/90506},
volume = {2},
year = {1997},
}

TY - JOUR
AU - Gámez, J. L.
AU - Montero, J. A.
TI - Uniqueness of the optimal control for a Lotka-Volterra control problem with a large crowding effect
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1997
PB - EDP Sciences
VL - 2
SP - 1
EP - 12
LA - eng
KW - admissible control; iterative approximation; optimal control; partial differential equation of Lotka-Volterra type; optimality system
UR - http://eudml.org/doc/90506
ER -

References

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  2. [2] H. Berestycki and P.L. Lions: Some applications of the method of super and subsolutions, Lect. Not. Math., 782, Springer-Verlag, 1980, 16-42. Zbl0433.35023MR572249
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  4. [4] A. Cañada, J.L. Gámez and J.A. Montero: An optimal control problem for a nonlinear elliptic equation arising from population dynamics, in Calculus of Variation, Applications and Computations, Longman, Pitman Research Notes in Mathematics Series, C. Bandle, J. Bemelmans, M. Chipot, J. Saint Jean Paulin and I. Shafrir, editors, 326, 1995, 35-40. Zbl0828.49006MR1419332
  5. [5] A. Cañada, J.L. Gámez and J.A. Montero: Study of a nonlinear optimal control problem for diffusive Volterra-Lotka equations, to appear. Zbl0916.49003
  6. [6] D. Gilbarg and N.S. Trudinger: Elliptic Partial Differential Equations of Second Order, 2nd Edition, Springer-Verlag, Berlin, 1983. Zbl0562.35001MR737190
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  8. [8] F. He, A. Leung and S. Stojanovic: Periodic optimal control for parabolic Volterra-Lotka type equations, Math. Methods Appl. Sci., 18, 1995, 127-146. Zbl0818.49002MR1311374
  9. [9] A. Leung: Systems of nonlinear partial differential equations, The Netherlands, Kluwer Acacemic Publishers, 1989. Zbl0691.35002MR1621827
  10. [10] A. Leung and S. Stojanovic: Direct methods for some distributed games, Diff. and Int. Eqns., 3, 1990, 1113-1125. Zbl0722.90093MR1073061
  11. [11] A. Leung and S. Stojanovic: Optimal control for elliptic Volterra-Lotka equations, J. Math. Anal. Appl., 173 1993, 603-619. Zbl0796.49005MR1209343
  12. [12] L. Li and R. Logan: Positive solutions to general elliptic competition models, Diff. and Int. Eqns., 4, 1991, 817-834. Zbl0751.35014MR1108062
  13. [13] S. Stojanovic: Optimal damping control and nonlinear elliptic Systems, SIAM J. Control Optim., 29, 1991, 594-608. Zbl0742.49017MR1089146
  14. [14] J. Smoller: Shock waves and reaction-diffusion equations, NewYork, Springer, 1983. Zbl0508.35002MR688146

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