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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.

Table of Contents

Frontmatter

Existence and Regularity Results, Quantitative Methods and Their Convergence

Frontmatter

2018 | OriginalPaper | Chapter

Chapter 1. Qualitative Methods for Classes of Nonlinear Systems: Constructive Existence Results

Michael Z. Zgurovsky, Pavlo O. Kasyanov

2018 | OriginalPaper | Chapter

Chapter 2. Regularity of Solutions for Nonlinear Systems

Michael Z. Zgurovsky, Pavlo O. Kasyanov

2018 | OriginalPaper | Chapter

Chapter 3. Advances in the 3D Navier-Stokes Equations

Michael Z. Zgurovsky, Pavlo O. Kasyanov

Convergence Results in Strongest Topologies

Frontmatter

2018 | OriginalPaper | Chapter

Chapter 4. Strongest Convergence Results for Weak Solutions of Non-autonomous Reaction-Diffusion Equations with Carathéodory’s Nonlinearity

Michael Z. Zgurovsky, Pavlo O. Kasyanov

2018 | OriginalPaper | Chapter

Chapter 5. Strongest Convergence Results for Weak Solutions of Feedback Control Problems

Michael Z. Zgurovsky, Pavlo O. Kasyanov

2018 | OriginalPaper | Chapter

Chapter 6. Strongest Convergence Results for Weak Solutions of Differential-Operator Equations and Inclusions

Michael Z. Zgurovsky, Pavlo O. Kasyanov

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

Frontmatter

2018 | OriginalPaper | Chapter

Chapter 7. Uniform Global Attractors for Non-autonomous Dissipative Dynamical Systems

Michael Z. Zgurovsky, Pavlo O. Kasyanov

2018 | OriginalPaper | Chapter

Chapter 8. Uniform Trajectory Attractors for Non-autonomous Nonlinear Systems

Michael Z. Zgurovsky, Pavlo O. Kasyanov

2018 | OriginalPaper | Chapter

Chapter 9. Indirect Lyapunov Method for Autonomous Dynamical Systems

Michael Z. Zgurovsky, Pavlo O. Kasyanov

Backmatter

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