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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 |
Tabla de Contenidos:
- 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.