Lecture notes on the mathematical theory of generalized Boltzmann models / Nicola Bellomo, Mauro Lo Schiavo.

Format:

Book

Author/Creator:

Bellomo, N.

Contributor:

Schiavo, Mauro Lo.

Series:

Series on Advances in Mathematics for Applied Sciences

Series on advances in mathematics for applied sciences ; vol. 51

Language:

English

Subjects (All):

Maxwell-Boltzmann distribution law.

Kinetic theory of matter--Mathematical models.

Kinetic theory of matter.

Physical Description:

1 online resource (355 p.)

Other Title:

Mathematical theory of generalized Boltzmann models

Place of Publication:

River Edge, NJ : World Scientific, c2000.

Language Note:

English

Summary:

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.

Contents:

2.3.5 Two conclusive examples2.4 Tools from Topology; 2.4.1 Basics on topologies; 2.4.2 Function spaces; 2.4.3 The linear spaces case; 2.5 References; Chapter 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; 3.5.1 Modelling η and ψ; 3.5.2 A model of social behaviors; 3.5.3 A model in epidemiology; 3.5.4 Perspectives; 3.6 References; Chapter 4 Generalized Kinetic Models for Coagulation and Fragmentation; 4.1 Introduction

4.2 Description of the Models4.3 Mathematical Problems; 4.3.1. Existence of solutions; 4.3.2. Equilibrium solutions and stability; 4.4 Critical Analysis and Perspectives; 4.5 References; Chapter 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; 5.5.1 Qualitative analysis; 5.5.2 Simulation problems; 5.5.3 Perspectives; 5.6 References

Chapter 6 Kinetic Models for the Evolution of Antigens Generalized Shape6.1 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; Chapter 7 The Boltzmann Model; 7.1 Introduction; 7.2 The Nonlinear Boltzmann Equation; 7.3 Mathematical Problems; 7.4 Analytic Treatment; 7.4.1 The Cauchy problem for small initial data; 7.4.2 The Cauchy problem for large initial data; 7.4.3 The initial-boundary value problem; 7.4.4 Open problems; 7.4.5 Evolution problems in the presence of a force field

7.4.6 Shock waves7.4.7 Asymptotic analysis; 7.5 Computational Methods; 7.6 References; Chapter 8 Generalized Kinetic Models for Traffic Flow; 8.1 Introduction; 8.2 Traffic Flow and Hydrodynamics; 8.2.1 Scalar hydrodynamic models; 8.2.2 Vector hydrodynamic models; 8.3 Kinetic Traffic Flow Models; 8.3.1 From Prigogine's to Paveri Fontana's modelling; 8.3.2 Developments in kinetic modelling; 8.3.3 Evolution problems; 8.4 Perspectives; 8.5 References; Chapter 9 Dissipative Kinetic Models for Disparate Mixtures; 9.1 Introduction; 9.2 Dissipative Collision Dynamics

9.2.1 Cluster conservative collisions

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9789812813336

9812813330

OCLC:

922951853