On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks

Autor: Carlo Bianca, Bruno Carbonaro, Marco Menale
Jazyk: angličtina
Rok vydání: 2020
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Zdroj: Symmetry, Vol 12, Iss 4, p 517 (2020)
Druh dokumentu: article
ISSN: 12040517
2073-8994
DOI: 10.3390/sym12040517
Popis: This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic theory frameworks for the modeling of nonequilibrium complex systems composed by particles whose microscopic state includes a vectorial state variable. The mathematical analysis refers to the global existence and uniqueness of the solution of the related Cauchy problem. Specifically, the paper is divided in two parts. In the first part the thermostatted framework with a continuous vectorial variable is proposed and analyzed. The framework consists of a system of partial integro-differential equations with quadratic type nonlinearities. In the second part the thermostatted framework with a discrete vectorial variable is investigated. Real world applications, such as social systems and crowd dynamics, and future research directions are outlined in the paper.
Databáze: Directory of Open Access Journals
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