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by Luisa Arlotti,Nicola Bellomo,Elena De Angelis,Miroslaw Lachowicz
Download Generalized Kinetic Models in Applied Sciences: Lecture Notes on Mathematical Problem (SERIES ON ADVANCES IN MATHEMATICS FOR APPLIED SCIENCES) (Vol 64) fb2
Mathematics
  • Author:
    Luisa Arlotti,Nicola Bellomo,Elena De Angelis,Miroslaw Lachowicz
  • ISBN:
    9812385606
  • ISBN13:
    978-9812385604
  • Genre:
  • Publisher:
    World Scientific Pub Co Inc (November 1, 2003)
  • Pages:
    220 pages
  • Subcategory:
    Mathematics
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Электронная книга "Generalized Kinetic Models in Applied Sciences: Lecture Notes on Mathematical Problems", Luisa Arlotti, Nicola Bellomo, Elena De Angelis, Miroslaw Lachowicz

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4. This work 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. 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.

Book Series There are 12 volumes in this series

Book Series There are 12 volumes in this series.

New & Forthcoming Titles Lecture Notes on Mathematical Modelling in. .

New & Forthcoming Titles Lecture Notes on Mathematical Modelling in the Life Sciences. New & Forthcoming Titles. Home New & Forthcoming Titles.

The evolution is determined both by interactions among individuals and by external actions

The evolution is determined both by interactions among individuals and by external actions

2 Nicola Bellomo Department of Mathematics Politecnico Torino Corso Duca Degli Abruzzi Torino, Italy Elena . Figure Diffusion in one space dimension. 12 6 Lectures Notes on Mathematical Modelling in Applied Sciences Using Eq yields: u t k 2 u 0 x, 2 k 0 h 0 (.

2 Nicola Bellomo Department of Mathematics Politecnico Torino Corso Duca Degli Abruzzi Torino, Italy Elena De Angelis Department of Mathematics Politecnico Torino Corso Duca Degli Abruzzi Torino, Italy Marcello Delitala Department of Mathematics Politecnico Torino Corso Duca Degli Abruzzi Torino, Italy. 6) c 0 The above model can also be used to describe the steady temperature distribution, which is obtained equating to zero the right-hand side term k 0 d 2 u dx 2 0

Nicola Bellomo Department of Mathematics Politecnico Torino Corso Duca Degli Abruzzi 24 10129 Torino, Italy . iv Lectures Notes on Mathematical Modelling in Applied Sciences . Critical Analysis.

iv Lectures Notes on Mathematical Modelling in Applied Sciences . 94 Chapter 3. Macroscopic Scale Models and Partial Differen- tial Equations .

Addresses the construction, analysis, and interpretation of mathematical models that shed light on significant problems in the physical . The authors' case studies approach leads to excitement in teaching realistic problems.

Addresses the construction, analysis, and interpretation of mathematical models that shed light on significant problems in the physical sciences. The exercises reinforce, test and extend the reader's understanding.

This book is the first one devoted to high-dimensional (or large-scale) .

This book is the first one devoted to high-dimensional (or large-scale) diffusion stochastic processes (DSPs) with nonlinear coefficients. of the Cauchy Problems for Ordinary Differential Equation System; Signal-to-Noise Ratio; Example of Application of Corollary . : Nonlinear Friction and Unbounded Stationary Probability Density of the Particle Velocity in Uniform Fluid; Proofs of the Theorems in Chapter 2 and Other Details; Proofs of the Theorems in Chapter 4; Hidden Randomness in Nonrandom Equation for the Particle Concentration of Uniform Fluid

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.