Qualitative and Quantitative Analysis of Nonlinear Systems
Theory and Applications
Authors: Zgurovsky, Michael Z., Kasyanov, Pavlo O.
Free Preview- Focuses on specific topics of nonlinear systems
- Includes constructive existence results and regularity theorems for all weak solutions
- Presents convergence results for solutions and their approximations in strongest topologies of the natural phase and extended phase spaces
- Explains uniform global behavior of solutions in time and pointwise behavior of solutions for autonomous problems with possible gaps by the phase variables
- Discusses numerous applications, including applied problems in physics, chemistry, biology and economics
- Is addressed to a wide readership from the fields of mathematics, mechanics and engineering
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- About this book
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Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems:
(a) constructive existence results and regularity theorems for all weak solutions;
(b) convergence results for solutions and their approximations;
(c) uniform global behavior of solutions in time; and
(d) pointwise behavior of solutions for autonomous problems with possible gaps by the phase variables. The general methodology for the investigation of dissipative dynamical systems with several applications including nonlinear parabolic equations of divergent form, nonlinear stochastic equations of parabolic type, unilateral problems, nonlinear PDEs on Riemannian manifolds with or without boundary, contact problems as well as particular examples is established. As such, the book is addressed to a wide circle of mathematical, mechanical and engineering readers.
- Reviews
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“This book presents a collection of known and new results on evolutional nonlinear systems which appear in a variety of applications in physics, mechanics, economy, biology and chemistry. … The book contains also a nice introduction on basic classes of problems presented with some historical comments. The entire book is clearly written, uses a modern notation and without a doubt it can be recommended to all researchers in this interesting field.” (Stanislaw Migórski, zbMATH 1402.93016, 2019)
- Table of contents (9 chapters)
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Qualitative Methods for Classes of Nonlinear Systems: Constructive Existence Results
Pages 3-45
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Regularity of Solutions for Nonlinear Systems
Pages 47-68
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Advances in the 3D Navier-Stokes Equations
Pages 69-86
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Strongest Convergence Results for Weak Solutions of Non-autonomous Reaction-Diffusion Equations with Carathéodory’s Nonlinearity
Pages 89-109
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Strongest Convergence Results for Weak Solutions of Feedback Control Problems
Pages 111-124
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Table of contents (9 chapters)
- Download Preface 1 PDF (49 KB)
- Download Sample pages 2 PDF (911.3 KB)
- Download Table of contents PDF (161.6 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Qualitative and Quantitative Analysis of Nonlinear Systems
- Book Subtitle
- Theory and Applications
- Authors
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- Michael Z. Zgurovsky
- Pavlo O. Kasyanov
- Series Title
- Studies in Systems, Decision and Control
- Series Volume
- 111
- Copyright
- 2018
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer International Publishing AG
- eBook ISBN
- 978-3-319-59840-6
- DOI
- 10.1007/978-3-319-59840-6
- Hardcover ISBN
- 978-3-319-59839-0
- Softcover ISBN
- 978-3-319-86715-1
- Series ISSN
- 2198-4182
- Edition Number
- 1
- Number of Pages
- XXXIII, 240
- Number of Illustrations
- 20 b/w illustrations, 23 illustrations in colour
- Topics
