## Optimal control for a nonlinear population dynamics problem.(English)Zbl 1082.92038

Summary: We consider a nonlinear age dependent and spatially structured population dynamic model. In this model the birth process is nonlocal and we investigate the existence of an optimal control which makes the density of the population as close as possible to some given density. Then, necessary optimality conditions in the case where the birth process is governed by the function $$F(\alpha)=c\alpha^2/(b+\alpha^2)$$ are investigated.

### MSC:

 92D25 Population dynamics (general) 49N90 Applications of optimal control and differential games 49J20 Existence theories for optimal control problems involving partial differential equations 49K20 Optimality conditions for problems involving partial differential equations
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