Series on Advances in Mathematics for Applied Sciences - Vol. 10
NONLINEAR EVOLUTION EQUATIONS
Kinetic Approach
by Niva B Maslova (Institute Oceanology, St Petersburg Branch, Russia)
The book is devoted to the questions of the long-time behavior of solutions for evolution equations, connected with kinetic models in statistical physics. There is a wide variety of problems where such models are used to obtain reasonable physical as well as numerical results (Fluid Mechanics, Gas Dynamics, Plasma Physics, Nuclear Physics, Turbulence Theory etc.). The classical examples provide the nonlinear Boltzmann equation. Investigation of the long-time behavior of the solutions for the Boltzmann equation gives an approach to the nonlinear fluid dynamic equations. From the viewpoint of dynamical systems, the fluid dynamic equations arise in the theory as a tool to describe an attractor of the kinetic equation.
Contents:
- Introduction
- Kinetic Approximations of Nonlinear Evolution
Equations. Formal Constructions
- Boltzmann Equation. Collision Operators
- Transport Operators
- Steady-State Solutions of the Linear Boltzmann Equation
- Nonlinear Steady-State Problems
- Initial-Boundary Value Problems for the Boltzmann Equation
Readership: Mathematicians, mathematical physicists, statistical physicists,
graduates and researchers.
"The book is an elegant summing-up of many results that are spread out in the literature."
"The book is a little gem which contains quite a few results that were difficult to find before, because they were published either not at all or only in Russian."
| 208pp |
Pub. date: Mar 1993 |
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