Lecture notes on the mathematical theory of generalized Boltzmann models

著者

書誌事項

Lecture notes on the mathematical theory of generalized Boltzmann models

Nicola Bellomo, Mauro Lo Schiavo

（Series on advances in mathematics for applied sciences, v. 51）

World Scientific, c2000

タイトル別名

The mathematical theory of generalized Boltzmann models

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions.Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.

目次

  • Generalized kinetic models
  • mathematical background - measure, integration, topology
  • models of population dynamics with stochastic interactions
  • generalized kinetic models for coagulation and fragmentation
  • kinetic cellular models in the immune system competition
  • kinetic models for the evolution of antigens generalized shape
  • the Boltzmann model
  • generalized kinetic models for traffic flow
  • dissipative kinetic models for disparate mixtures
  • research perspectives.

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