Abstract
We analyze a system of nonlinear partial differential equations modeling the dynamics of certain mosquito populations by taking in consideration the iterations among the immature (aquatic) subpopulation, the adult winged subpopulation and the environment resources; the immature subpopulation is assumed to be age-structured and the model also considers the action of control mechanisms on these subpopulations.After a first analysis on the existence and uniqueness of solutions for the model, we use the obtained results to prove the existence of an optimal solution of a given optimal control problem. The corresponding first order optimality conditions are also rigorously obtained by approximating our original optimal control problem by pure optimization problems obtained by using penalization arguments.
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