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Qualitative and Quantitative Analysis of Nonlinear Systems

Theory and Applications

  • Michael Z. Zgurovsky
  • Pavlo O. Kasyanov

Part of the Studies in Systems, Decision and Control book series (SSDC, volume 111)

Table of contents

  1. Front Matter
    Pages i-xxxiii
  2. Existence and Regularity Results, Quantitative Methods and Their Convergence

    1. Front Matter
      Pages 1-1
    2. Michael Z. Zgurovsky, Pavlo O. Kasyanov
      Pages 47-68
    3. Michael Z. Zgurovsky, Pavlo O. Kasyanov
      Pages 69-86
  3. Convergence Results in Strongest Topologies

  4. Uniform Global Behavior of Solutions: Uniform Attractors, Flattening and Entropy

    1. Front Matter
      Pages 159-159
    2. Michael Z. Zgurovsky, Pavlo O. Kasyanov
      Pages 161-177
    3. Michael Z. Zgurovsky, Pavlo O. Kasyanov
      Pages 179-210
    4. Michael Z. Zgurovsky, Pavlo O. Kasyanov
      Pages 211-237
  5. Back Matter
    Pages 239-240

About this book

Introduction

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.

Keywords

Nonlinear Systems Qualitative Analysis Numerical Analysis Regularity Complex Systems

Authors and affiliations

  • Michael Z. Zgurovsky
    • 1
  • Pavlo O. Kasyanov
    • 2
  1. 1.Igor Sikorsky Kyiv Polytechnic InstituteKyivUkraine
  2. 2.Institute for Applied System AnalysisIgor Sikorsky Kyiv Polytechnic InstituteKyivUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-59840-6
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-59839-0
  • Online ISBN 978-3-319-59840-6
  • Series Print ISSN 2198-4182
  • Series Online ISSN 2198-4190
  • Buy this book on publisher's site
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