Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Studies in Systems, Decision and Control (SSDC, volume 111)
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Table of contents (9 chapters)
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Front Matter
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Existence and Regularity Results, Quantitative Methods and Their Convergence
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Front Matter
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Convergence Results in Strongest Topologies
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Front Matter
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Uniform Global Behavior of Solutions: Uniform Attractors, Flattening and Entropy
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Front Matter
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Back Matter
Keywords
About this book
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.
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Authors and Affiliations
Bibliographic Information
Book Title: Qualitative and Quantitative Analysis of Nonlinear Systems
Book Subtitle: Theory and Applications
Authors: Michael Z. Zgurovsky, Pavlo O. Kasyanov
Series Title: Studies in Systems, Decision and Control
DOI: https://doi.org/10.1007/978-3-319-59840-6
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing AG 2018
Hardcover ISBN: 978-3-319-59839-0Published: 18 July 2017
Softcover ISBN: 978-3-319-86715-1Published: 02 August 2018
eBook ISBN: 978-3-319-59840-6Published: 11 July 2017
Series ISSN: 2198-4182
Series E-ISSN: 2198-4190
Edition Number: 1
Number of Pages: XXXIII, 240
Number of Illustrations: 20 b/w illustrations, 23 illustrations in colour
Topics: Computational Intelligence, Complexity, Applications of Nonlinear Dynamics and Chaos Theory, Control and Systems Theory