Год выпуска: 2010 Автор: Igor Gaissinski and Vladimir Rovenski Издательство: LAP Lambert Academic Publishing Страниц: 700 ISBN: 9783843366557
Описание
Nonlinear phenomena and instabilities arise in all fields of physics, chemistry, biology, and engineering. The book consists of six chapters. Chapter 1 contains preliminary topics from analysis: elements of set theory, measure theory, integration theory, asymptotic expansions, continued fractions and Pad''e approximations. Chapters 2 and 3 are devoted to basic and advanced methods of ODE''s and their visualization: attractors, fractals, bifurcations, chaos, and elements of stability theory. Chapter 4 studies analytical and geometrical aspects of perturbation theory and contains many examples. Chapter 5 represents the basic knowledge in turbulence theory and introduces to Richardson-Kolmogorov concept, deals with bifurcations in Kuramoto-Sivashinsky equation, and develops multifractal and hierarchical (shell) models of turbulence. The main hydrodynamic instabilities (Rayleigh-Taylor, Kelvin-Helmholtz, and Richtmyer-Meshkov) are studied in Chapter 6. The book contains theoretical and...