The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems.

In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed.

The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.

Contents:

• Preface


• Introduction


• Preliminaries


• Semilinear Equations


• Convergence of Attractors


• Convergence of Attractors in the Hyperbolic Case


• Shadowing for Abstract Parabolic Equations


• Semilinear Fractional Equations


• Stable and Unstable Manifolds for Fractional Semilinear Equations


• Bibliography


• Index

Readership: This book is addressed to graduate and postgraduate students specialized in functional analysis, approximation of abstract differential equations, and dynamical systems. It is also useful for mathematicians and physicists working in these and related areas.

Key Features:

• In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book


• The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed