Stability and optimization in structured population models on graphs

Rinaldo M. Colombo; Mauro Garavello

doi:10.3934/mbe.2015.12.311

Article Contents

2015, Volume 12, Issue 2: 311-335. Doi: 10.3934/mbe.2015.12.311 open access

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Stability and optimization in structured population models on graphs

Rinaldo M. Colombo^1, and
Mauro Garavello^2,

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

Received: April 2014

Revised: July 2014

Published: November 2014

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Abstract

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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Mathematics Subject Classification: Primary: 35L50; Secondary: 92D25.

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