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The Scientific World Journal
Volume 2013, Article ID 274719, 6 pages
http://dx.doi.org/10.1155/2013/274719
Research Article

Controllability in Hybrid Kinetic Equations Modeling Nonequilibrium Multicellular Systems

Dipartimento di Scienze Matematiche, Politecnico, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Received 8 August 2013; Accepted 2 September 2013

Academic Editors: K. Ammari, M. M. Cavalcanti, and S. Sivasundaram

Copyright © 2013 Carlo Bianca. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the derivation of hybrid kinetic partial integrodifferential equations that can be proposed for the mathematical modeling of multicellular systems subjected to external force fields and characterized by nonconservative interactions. In order to prevent an uncontrolled time evolution of the moments of the solution, a control operator is introduced which is based on the Gaussian thermostat. Specifically, the analysis shows that the moments are solution of a Riccati-type differential equation.