We introduce a class of set evolution equations that can be used to describe population's movements as well as various instances of individual-population interactions. Optimal control/management problems can be formalized and tackled in this framework. A rigorous analytical structure is established and the basic well posedness results are obtained. Several examples show possible applications and their numerical integrations display possible qualitative behaviors of solutions.
On the modeling of moving populations through set evolution equations
Pogodaev N. I.
2015
Abstract
We introduce a class of set evolution equations that can be used to describe population's movements as well as various instances of individual-population interactions. Optimal control/management problems can be formalized and tackled in this framework. A rigorous analytical structure is established and the basic well posedness results are obtained. Several examples show possible applications and their numerical integrations display possible qualitative behaviors of solutions.
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