Optimal Control for the Degenerate Elliptic Logistic Equation |
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| Affiliation: | (1) Departamento Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, C/ Tarfia s/n, C.P. 41012, Universidad de Sevilla, Sevilla, Spain {delgado, suarez}@numer.us.es, ES;(2) Departamento Análisis Matemático, C.P. 18071, Universidad de Granada, Granada, Spain jmontero@goliat.ugr.es Communicated by R. Triggiani, ES |
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| Abstract: | We consider the optimal control of harvesting the diffusive degenerate elliptic logistic equation. Under certain assumptions, we prove the existence and uniqueness of an optimal control. Moreover, the optimality system and a characterization of the optimal control are also derived. The sub-supersolution method, the singular eigenvalue problem and differentiability with respect to the positive cone are the techniques used to obtain our results. |
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| Keywords: | . Degenerate logistic equation Singular eigenvalue problems Optimal control. AMS Classification. Primary 49J20 49K20 92D25 Secondary 35J65. |
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