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On the Self-Similar Asymptotics for Generalized Nonlinear Kinetic Maxwell Models
Karlstad University, Faculty of Technology and Science, Department of Mathematics. (Kinetisk teori)
Politecnico di Milano.
Department of Mathematics, The University of Texas at Austin.
2009 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 291, no 3, 599-644 p.Article in journal (Refereed) Published
Abstract [en]

Maxwell models for nonlinear kinetic equations have many applications in physics, dynamics of granular gases, economics, etc. In the present manuscript we consider such models from a very general point of view, including those with arbitrary polynomial non-linearities and in any dimension space. It is shown that the whole class of generalized Maxwell models satisfies properties one of which can be interpreted as an operator generalization of usual Lipschitz conditions. This property allows to describe in detail a behavior of solutions to the corresponding initial value problem. In particular, we prove in the most general case an existence of self similar solutions and study the convergence, in the sense of probability measures, of dynamically scaled solutions to the Cauchy problem to those self-similar solutions, as time goes to infinity. A new application of multi-linear models to economics and social dynamics is discussed

Place, publisher, year, edition, pages
Springer, 2009. Vol. 291, no 3, 599-644 p.
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-9920DOI: 10.1007/s00220-009-0876-3OAI: oai:DiVA.org:kau-9920DiVA: diva2:493430
Funder
Swedish Research Council, 621-2006-3404
Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2012-12-04Bibliographically approved

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