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Lecture notes on the mathematical theory of generalized Boltzmann models /
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 ove...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
River Edge, NJ :
World Scientific,
©2000.
|
| Colección: | Series on advances in mathematics for applied sciences ;
v. 51. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Bellomo, N. | |
| 245 | 1 | 0 | |a Lecture notes on the mathematical theory of generalized Boltzmann models / |c Nicola Bellomo, Mauro Lo Schiavo. |
| 246 | 3 | 0 | |a Mathematical theory of generalized Boltzmann models |
| 260 | |a River Edge, NJ : |b World Scientific, |c ©2000. | ||
| 300 | |a 1 online resource (xiii, 334 pages) : |b illustrations | ||
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| 490 | 1 | |a Series on advances in mathematics for applied sciences ; |v v. 51 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Ch. 1. Generalized kinetic models. 1.1. Introduction. 1.2. Generalized kinetic models. 1.3. Generalized models and plan of the book. 1.4. Aim of the book. 1.5. References -- ch. 2. Mathematical background: Measure, integration, topology. 2.1. Introduction. 2.2. Tools from measure theory. 2.3. Tools from integration Th. 2.4. Tools from topology. 2.5. References -- ch. 3. Models of population dynamics with stochastic interactions. 3.1. Introduction. 3.2. The generalized Jager and Segel model. 3.3. On the initial value problem. 3.4. Stationary points. 3.5. Applications and perspectives. 3.6. References -- ch. 4. Generalized kinetic models for coagulation and fragmentation. 4.1. Introduction. 4.2. Description of the models. 4.3. Mathematical problems. 4.4. Critical analysis and perspectives. 4.5. References -- ch. 5. Kinetic cellular models in the immune system competition. 5.1. Kinetic models towards immunology. 5.2. Scaling in kinetic cellular models. 5.3. Phenomenological system and modelling. 5.4. Kinetic evolution equations. 5.5. Qualitative analysis, applications, and perspectives. 5.6. References -- ch. 6. Kinetic models for the evolution of antigens generalized shape. 6.1. An introduction to the generalized shape. 6.2. The mathematical model. 6.3. On the initial value problem. 6.4. Applications and developments. 6.5. References -- ch. 7. The Boltzmann model. 7.1. Introduction. 7.2. The nonlinear Boltzmann equation. 7.3. Mathematical problems. 7.4. Analytic treatment. 7.5. Computational methods. 7.6. References -- ch. 8. Generalized kinetic models for traffic flow. 8.1. Introduction. 8.2. Traffic flow and hydrodynamics. 8.4. Perspectives. 8.5. References -- ch. 9. Dissipative kinetic models for disparate mixtures. 9.1. Introduction. 9.2. Dissipative collision dynamics. 9.3. Kinetic equations for mixtures of clusters. 9.4. Mixtures with continuous mass distribution. 9.5. Mathematical problems. 9.6. Perspectives in modelling. 9.7. References -- ch. 10. Research perspectives. 10.1. Introduction. 10.2. Discrete generalized models. 10.3. Looking for a general structure. 10.4. Development of new models. 10.5. Closure. 10.6. References. | |
| 520 | |a 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. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Maxwell-Boltzmann distribution law. | |
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| 650 | 6 | |a Distribution de Maxwell-Boltzmann. | |
| 650 | 6 | |a Théorie cinétique de la matière |x Modèles mathématiques. | |
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| 650 | 7 | |a Maxwell-Boltzmann distribution law. |2 fast |0 (OCoLC)fst01012685 | |
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| 650 | 7 | |a Matière, Théorie cinétique de la. |2 ram | |
| 700 | 1 | |a Schiavo, Mauro Lo. | |
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