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Nonlinear Problems: Present and Future
Nonlinear Problems: Present and Future
Advances in Wave Interaction and Turbulence
We often think of our natural environment as being composed of very many interacting particles, undergoing individual chaotic motions, of which only very coarse averages are perceptible at scales natural to us. However, we could as well think of the world as being made out of individual waves. This is so not just because the distinction between waves and particles becomes rather blurred at the atomic level, but also because even phenomena at much larger scales are better describedin terms of waves rather than of particles: It is rare in both fluids and solids to observe energy being carried from one region of space to another by a given set of material particles; much more often, this transf...
Turbulence in Fluid Flows
The articles in this volume are based on recent research on the phenomenon of turbulence in fluid flows collected by the Institute for Mathematics and its Applications. This volume looks into the dynamical properties of the solutions of the Navier-Stokes equations, the equations of motion of incompressible, viscous fluid flows, in order to better understand this phenomenon. Although it is a basic issue of science, it has implications over a wide spectrum of modern technological applications. The articles offer a variety of approaches to the Navier-Stokes problems and related issues. This book should be of interest to both applied mathematicians and engineers.
Pattern Formation in Continuous and Coupled Systems
This IMA Volume in Mathematics and its Applications PATTERN FORMATION IN CONTINUOUS AND COUPLED SYSTEMS is based on the proceedings of a workshop with the same title, but goes be yond the proceedings by presenting a series of mini-review articles that sur vey, and provide an introduction to, interesting problems in the field. The workshop was an integral part of the 1997-98 IMA program on "EMERG ING APPLICATIONS OF DYNAMICAL SYSTEMS." I would like to thank Martin Golubitsky, University of Houston (Math ematics) Dan Luss, University of Houston (Chemical Engineering), and Steven H. Strogatz, Cornell University (Theoretical and Applied Mechan ics) for their excellent work as organizers of the m...
Large-scale Atmosphere-ocean Dynamics: Analytical methods and numerical models
Publisher Description
Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations
This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in 1986 and 1987. Our aim was to present a direct geometric approach in the theory of inertial manifolds (global analogs of the unstable-center manifolds) for dissipative partial differential equations. This approach, based on Cauchy integral mani folds for which the solutions of the partial differential equations are the generating characteristic curves, has the advantage that it provides a sound basis for numerical Galerkin schemes obtained by approximating the inertial manifold. The work is self-contained and the prerequisites are at the level of a graduate student. The theoretical part of the work is developed in Chapters 2-14, while in Chapters 15-19 we apply the theory to several remarkable partial differ ential equations.
Infinite-Dimensional Dynamical Systems in Mechanics and Physics
In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.
Handbook of Mathematical Fluid Dynamics
The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.
Nonlinear Partial Differential Equations And Applications: Proceedings Of The Conference
Contents: Direct and Inverse Diffraction by Periodic Structures (G Bao)Weak Flow of H-Systems (Y-M Chen)Strongly Compact Attractor for Dissipative Zakharov Equations (B-L Guo et al.)C∞-Solutions of Generalized Porous Medium Equations (M Ôtani & Y Sugiyama)Cauchy Problem for Generalized IMBq Equation (G-W Chen & S-B Wang)Inertial Manifolds for a Nonlocal Kuramoto–Sivashinsky Equation (J-Q Duan et al.)Weak Solutions of the Generalized Magnetic Flow Equations (S-H He & Z-D Dai)The Solution of Hammerstein Integral Equation Without Coercive Conditions (Y-L Shu)Global Behaviour of the Solution of Nonlinear Forest Evolution Equation (D-J Wang)Uniqueness of Generalized Solutions for Semiconduct...
