Mathematical Biosciences and Engineering, 2015, 12(2): 311-335. doi: 10.3934/mbe.2015.12.311.

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Stability and optimization in structured population models on graphs

1. INdAM Unit, University of Brescia, Brescia
2. Department of Mathematics and Applications, University of Milano-Bicocca, Via R. Cozzi, 53, 20125 Milano

We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular choice of the boundary condition allows to comprehend models with very different structures. In particular, we consider a juvenile-adult model, the problem of the optimal mating ratio and a model for the optimal management of biological resources. The stability result obtained allows to tackle various optimal management/control problems, providing sufficient conditions for the existence of optimal choices/controls.
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Keywords optimal mating ratio.; management of biological resources; juvenile-adult model; Renewal equation; balance laws

Citation: Rinaldo M. Colombo, Mauro Garavello. Stability and optimization in structured population models on graphs. Mathematical Biosciences and Engineering, 2015, 12(2): 311-335. doi: 10.3934/mbe.2015.12.311

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This article has been cited by

  • 1. Rinaldo M. Colombo, Mauro Garavello, Well Posedness and Control in a NonLocal SIR Model, Applied Mathematics & Optimization, 2020, 10.1007/s00245-020-09660-9
  • 2. G.M. Coclite, C. Donadello, T.N.T. Nguyen, A PDE model for the spatial dynamics of a voles population structured in age, Nonlinear Analysis, 2020, 196, 111805, 10.1016/j.na.2020.111805

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Copyright Info: 2015, Rinaldo M. Colombo, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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