Attractors, Shadowing, And Approximation Of Abstract Semilinear Differential Equations
Title | Attractors, Shadowing, And Approximation Of Abstract Semilinear Differential Equations PDF eBook |
Author | Sergey I Piskarev |
Publisher | World Scientific |
Pages | 213 |
Release | 2023-07-05 |
Genre | Mathematics |
ISBN | 9811272794 |
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.
Attractors for Equations of Mathematical Physics
Title | Attractors for Equations of Mathematical Physics PDF eBook |
Author | Vladimir V. Chepyzhov |
Publisher | American Mathematical Soc. |
Pages | 377 |
Release | 2002 |
Genre | Mathematics |
ISBN | 0821829505 |
One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behavior of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For anumber of basic evolution equations of mathematical physics, it was shown that the long time behavior of their solutions can be characterized by a very important notion of a global attractor of the equation. In this book, the authors study new problems related to the theory of infinite-dimensionaldynamical systems that were intensively developed during the last 20 years. They construct the attractors and study their properties for various non-autonomous equations of mathematical physics: the 2D and 3D Navier-Stokes systems, reaction-diffusion systems, dissipative wave equations, the complex Ginzburg-Landau equation, and others. Since, as it is shown, the attractors usually have infinite dimension, the research is focused on the Kolmogorov $\varepsilon$-entropy of attractors. Upperestimates for the $\varepsilon$-entropy of uniform attractors of non-autonomous equations in terms of $\varepsilon$-entropy of time-dependent coefficients are proved. Also, the authors construct attractors for those equations of mathematical physics for which the solution of the corresponding Cauchyproblem is not unique or the uniqueness is not proved. The theory of the trajectory attractors for these equations is developed, which is later used to construct global attractors for equations without uniqueness. The method of trajectory attractors is applied to the study of finite-dimensional approximations of attractors. The perturbation theory for trajectory and global attractors is developed and used in the study of the attractors of equations with terms rapidly oscillating with respect tospatial and time variables. It is shown that the attractors of these equations are contained in a thin neighborhood of the attractor of the averaged equation. The book gives systematic treatment to the theory of attractors of autonomous and non-autonomous evolution equations of mathematical physics.It can be used both by specialists and by those who want to get acquainted with this rapidly growing and important area of mathematics.
Shadowing in Dynamical Systems
Title | Shadowing in Dynamical Systems PDF eBook |
Author | Sergei Yu. Pilyugin |
Publisher | Springer |
Pages | 284 |
Release | 2006-11-14 |
Genre | Mathematics |
ISBN | 3540484299 |
This book is an introduction to the theory of shadowing of approximate trajectories in dynamical systems by exact ones. This is the first book completely devoted to the theory of shadowing. It shows the importance of shadowing theory for both the qualitative theory of dynamical systems and the theory of numerical methods. Shadowing Methods allow us to estimate differences between exact and approximate solutions on infinite time intervals and to understand the influence of error terms. The book is intended for specialists in dynamical systems, for researchers and graduate students in the theory of numerical methods.
Global Attractors in Abstract Parabolic Problems
Title | Global Attractors in Abstract Parabolic Problems PDF eBook |
Author | Jan W. Cholewa |
Publisher | Cambridge University Press |
Pages | 252 |
Release | 2000-08-31 |
Genre | Mathematics |
ISBN | 0521794242 |
This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations.
Handbook of Differential Equations: Evolutionary Equations
Title | Handbook of Differential Equations: Evolutionary Equations PDF eBook |
Author | C.M. Dafermos |
Publisher | Elsevier |
Pages | 609 |
Release | 2008-10-06 |
Genre | Mathematics |
ISBN | 0080931979 |
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts
Discrete and Continuous Dynamical Systems
Title | Discrete and Continuous Dynamical Systems PDF eBook |
Author | |
Publisher | |
Pages | 752 |
Release | 2008 |
Genre | Dynamics |
ISBN |
Mathematical Reviews
Title | Mathematical Reviews PDF eBook |
Author | |
Publisher | |
Pages | 1884 |
Release | 2005 |
Genre | Mathematics |
ISBN |