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Optimal strategies for a time-dependent harvesting problem
1. | Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy |
2. | Department of Mathematics and its Applications, University of Milano Bicocca, Via R. Cozzi 55, 20125 Milano, Italy |
3. | IMATI-CNR, Via Ferrata 1, 27100 Pavia, Italy |
We focus on an optimal control problem, introduced by Bressan and Shen in [
References:
[1] |
L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford University Press, New York, 2000.
![]() ![]() |
[2] |
O. Arino and J. A. Montero,
Optimal control of a nonlinear elliptic population system, Proc. Edinburgh Math. Soc., 43 (2000), 225-241.
doi: 10.1017/S0013091500020897. |
[3] |
L. Boccardo and T. Gallouët,
Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal., 87 (1989), 149-169.
doi: 10.1016/0022-1236(89)90005-0. |
[4] |
A. Bressan, G. M. Coclite and W. Shen,
A multi-dimensional optimal harvesting problem with measure valued solutions, SIAM J. Control Optim., 51 (2013), 1186-1202.
doi: 10.1137/110853510. |
[5] |
A. Bressan and W. Shen,
Measure-valued solutions for a differential game related to fish harvesting, SIAM J. Control Optim., 47 (2008), 3118-3137.
doi: 10.1137/07071007X. |
[6] |
A. Bressan and W. Shen,
Measure valued solutions to a harvesting game with several players, Advances in Dynamic Games, 11 (2011), 399-423.
doi: 10.1007/978-0-8176-8089-3_20. |
[7] |
J. R. Cannon, The One-Dimensional Heat Equation, With a foreword by Felix E. Browder.
Encyclopedia of Mathematics and its Applications, 23. Addison-Wesley Publishing Company,
Advanced Book Program, Reading, MA, 1984.
doi: 10.1017/CBO9781139086967. |
[8] |
A. Cañada, J. L. Gámez and J. A. Montero,
Study of an optimal control problem for diffusive nonlinear elliptic equations of logistic type, SIAM J. Control Optim., 36 (1998), 1171-1189.
doi: 10.1137/S0363012995293323. |
[9] |
G. M. Coclite and M. Garavello,
A time dependent optimal harvesting problem with measure valued solutions, SIAM J. Control Optim., 55 (2017), 913-935.
doi: 10.1137/16M1061886. |
[10] |
M. Delgado, J. A. Montero and A. Suárez,
Optimal control for the degenerate elliptic logistic equation, Appl. Math. Optim., 45 (2002), 325-345.
doi: 10.1007/s00245-001-0039-1. |
[11] |
M. Delgado, J. A. Montero and A. Suárez,
Study of the optimal harvesting control and the optimality system for an elliptic problem, SIAM J. Control Optim., 42 (2003), 1559-1577.
doi: 10.1137/S0363012902410903. |
[12] |
S. M. Lenhart and J. A. Montero,
Optimal control of harvesting in a parabolic system modeling two subpopulations, Math. Models Methods Appl. Sci., 11 (2001), 1129-1141.
doi: 10.1142/S0218202501000982. |
[13] |
S. Salsa, Partial Differential Equations in Action. From Modelling to Theory, Universitext. Springer-Verlag Italia, Milan, 2008. |
[14] |
J. Simon,
Compact sets in the space $L_p (0, T ; B)$, Ann. Mat. Pura Appl. (4), 146 (1987), 65-96.
doi: 10.1007/BF01762360. |
show all references
References:
[1] |
L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford University Press, New York, 2000.
![]() ![]() |
[2] |
O. Arino and J. A. Montero,
Optimal control of a nonlinear elliptic population system, Proc. Edinburgh Math. Soc., 43 (2000), 225-241.
doi: 10.1017/S0013091500020897. |
[3] |
L. Boccardo and T. Gallouët,
Nonlinear elliptic and parabolic equations involving measure data, J. Funct. Anal., 87 (1989), 149-169.
doi: 10.1016/0022-1236(89)90005-0. |
[4] |
A. Bressan, G. M. Coclite and W. Shen,
A multi-dimensional optimal harvesting problem with measure valued solutions, SIAM J. Control Optim., 51 (2013), 1186-1202.
doi: 10.1137/110853510. |
[5] |
A. Bressan and W. Shen,
Measure-valued solutions for a differential game related to fish harvesting, SIAM J. Control Optim., 47 (2008), 3118-3137.
doi: 10.1137/07071007X. |
[6] |
A. Bressan and W. Shen,
Measure valued solutions to a harvesting game with several players, Advances in Dynamic Games, 11 (2011), 399-423.
doi: 10.1007/978-0-8176-8089-3_20. |
[7] |
J. R. Cannon, The One-Dimensional Heat Equation, With a foreword by Felix E. Browder.
Encyclopedia of Mathematics and its Applications, 23. Addison-Wesley Publishing Company,
Advanced Book Program, Reading, MA, 1984.
doi: 10.1017/CBO9781139086967. |
[8] |
A. Cañada, J. L. Gámez and J. A. Montero,
Study of an optimal control problem for diffusive nonlinear elliptic equations of logistic type, SIAM J. Control Optim., 36 (1998), 1171-1189.
doi: 10.1137/S0363012995293323. |
[9] |
G. M. Coclite and M. Garavello,
A time dependent optimal harvesting problem with measure valued solutions, SIAM J. Control Optim., 55 (2017), 913-935.
doi: 10.1137/16M1061886. |
[10] |
M. Delgado, J. A. Montero and A. Suárez,
Optimal control for the degenerate elliptic logistic equation, Appl. Math. Optim., 45 (2002), 325-345.
doi: 10.1007/s00245-001-0039-1. |
[11] |
M. Delgado, J. A. Montero and A. Suárez,
Study of the optimal harvesting control and the optimality system for an elliptic problem, SIAM J. Control Optim., 42 (2003), 1559-1577.
doi: 10.1137/S0363012902410903. |
[12] |
S. M. Lenhart and J. A. Montero,
Optimal control of harvesting in a parabolic system modeling two subpopulations, Math. Models Methods Appl. Sci., 11 (2001), 1129-1141.
doi: 10.1142/S0218202501000982. |
[13] |
S. Salsa, Partial Differential Equations in Action. From Modelling to Theory, Universitext. Springer-Verlag Italia, Milan, 2008. |
[14] |
J. Simon,
Compact sets in the space $L_p (0, T ; B)$, Ann. Mat. Pura Appl. (4), 146 (1987), 65-96.
doi: 10.1007/BF01762360. |
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