The paper deals with the harvesting model introduced by one of the authors in a joint paper with A. Bressan and W. Shen. A cost term which plays an essential role in the existence proof is removed here leading to some new phenomena. Since a solution not always exists in this case, we propose a relaxed version of the problem which is always solvable, has a geometrical interpretation in the functions space and whose unique solution, under suitable conditions, solves also the original problem. Finally, the notion of strategy limit of a sequence of smooth measures is introduced as a long-term control to fish populations.
Measure valued solutions for an optimal harvesting problem / Coclite, Giuseppe Maria; Devillanova, Giuseppe; Solimini, Sergio. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - STAMPA. - 142:(2020), pp. 204-228. [10.1016/j.matpur.2020.08.004]
Measure valued solutions for an optimal harvesting problem
Giuseppe Maria Coclite
;Giuseppe Devillanova;Sergio Solimini
2020-01-01
Abstract
The paper deals with the harvesting model introduced by one of the authors in a joint paper with A. Bressan and W. Shen. A cost term which plays an essential role in the existence proof is removed here leading to some new phenomena. Since a solution not always exists in this case, we propose a relaxed version of the problem which is always solvable, has a geometrical interpretation in the functions space and whose unique solution, under suitable conditions, solves also the original problem. Finally, the notion of strategy limit of a sequence of smooth measures is introduced as a long-term control to fish populations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.