Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 13, Issue 6, Pages 2593-2608Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2012.03.005
Keywords
Complexity; Population dynamics; Mathematical biology; Dynamical Systems; Nonlinear ODE and PDE
Categories
Funding
- FIRB [RBID08PP3J]
- INDAM-GNFM [43]
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This paper is concerned with the derivation of a new discrete general framework of the kinetic theory, suitable for the modeling of complex systems under the action of an external force field and constrained to kept constant the mass or density, and the kinetic or activation energy. The resulting model relies on the interactions of single individuals within the population and is expressed by means of nonlinear ordinary or partial integro-differential equations. The global in time existence and uniqueness of the solution to the relative Cauchy problem are proved for which the density and the energy of the solution are preserved. A critical analysis, proposed in the last part of the paper, outlines suitable applications and research perspectives. (C) 2012 Elsevier Ltd. All rights reserved.
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