Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models write by N. Bellomo. This book was released on 2000. Lecture Notes on the Mathematical Theory of Generalized Boltzmann Models available in PDF, EPUB and Kindle. 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.
Generalized Kinetic Models In Applied Sciences: Lecture Notes On Mathematical Problems
Generalized Kinetic Models In Applied Sciences: Lecture Notes On Mathematical Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Generalized Kinetic Models In Applied Sciences: Lecture Notes On Mathematical Problems write by Luisa Arlotti. This book was released on 2003-08-12. Generalized Kinetic Models In Applied Sciences: Lecture Notes On Mathematical Problems available in PDF, EPUB and Kindle. This book deals with analytic problems related to some developments and generalizations of the Boltzmann equation toward the modeling and qualitative analysis of large systems that are of interest in applied sciences. These generalizations are documented in the various surveys edited by Bellomo and Pulvirenti with reference to models of granular media, traffic flow, mathematical biology, communication networks, and coagulation models.The above literature motivates applied mathematicians to study the Cauchy problem and to develop an asymptotic analysis for models regarded as developments of the Boltzmann equation. This book aims to initiate the research plan by the analyzing afore mentioned analysis problems.The first generalization dealt with refers to the averaged Boltzmann equation, which is obtained by suitable averaging of the distribution function of the field particles into the action domain of the test particle. This model is further developed to describe equations with dissipative collisions and a class of models that are of interest in mathematical biology. In this latter case the state of the particles is defined not only by a mechanical variable but also by a biological microscopic state.The book is essentially devoted to analytic aspects and deals with the analysis of the Cauchy problem and with the development of an asymptotic theory to obtain the macroscopic description from the mesoscopic one.
Generalized Kinetic Models in Applied Sciences
Generalized Kinetic Models in Applied Sciences - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Generalized Kinetic Models in Applied Sciences write by Luisa Arlotti. This book was released on 2003. Generalized Kinetic Models in Applied Sciences available in PDF, EPUB and Kindle. This book deals with analytic problems related to some developments and generalizations of the Boltzmann equation toward the modeling and qualitative analysis of large systems that are of interest in applied sciences. These generalizations are documented in the various surveys edited by Bellomo and Pulvirenti with reference to models of granular media, traffic flow, mathematical biology, communication networks, and coagulation models. The first generalization dealt with refers to the averaged Boltzmann equation, which is obtained by suitable averaging of the distribution function of the field particles into the action domain of the test particle. This model is further developed to describe equations with dissipative collisions and a class of models that are of interest in mathematical biology. In this latter case the state of the particles is defined not only by a mechanical variable but also by a biological microscopic state.
Lecture Notes on the Discretization of the Boltzmann Equation
Lecture Notes on the Discretization of the Boltzmann Equation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lecture Notes on the Discretization of the Boltzmann Equation write by N. Bellomo. This book was released on 2003. Lecture Notes on the Discretization of the Boltzmann Equation available in PDF, EPUB and Kindle. This book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community.
High-dimensional Nonlinear Diffusion Stochastic Processes
High-dimensional Nonlinear Diffusion Stochastic Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook High-dimensional Nonlinear Diffusion Stochastic Processes write by Yevgeny Mamontov. This book was released on 2001. High-dimensional Nonlinear Diffusion Stochastic Processes available in PDF, EPUB and Kindle. Annotation This book is one of the first few devoted to high-dimensional diffusion stochastic processes with nonlinear coefficients. These processes are closely associated with large systems of Ito's stochastic differential equations and with discretized-in-the-parameter versions of Ito's stochastic differential equations that are nonlocally dependent on the parameter. The latter models include Ito's stochastic integro-differential, partial differential and partial integro-differential equations.The book presents the new analytical treatment which can serve as the basis of a combined, analytical -- numerical approach to greater computational efficiency. Some examples of the modelling of noise in semiconductor devices are provided
