Asymptotic Behaviour of Solutions of Evolutionary Equations ( Lezioni Lincee )

Publication series ：Lezioni Lincee

Author： M. I. Vishik  

Publisher： Cambridge University Press‎

Publication year： 1993

E-ISBN: 9780511881374

P-ISBN(Paperback): 9780521420235

Subject： O175.2 Partial Differential Equations

Keyword： 微分方程、积分方程

Language： ENG

Access to resources Favorite

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Asymptotic Behaviour of Solutions of Evolutionary Equations

Description

The theme of this book is the investigation of globally asymptotic solutions of evolutionary equations. Locally asymptotic solutions of the Navier–Stokes equations and reaction-diffusion equations are the starting point, and by considering perturbed evolutionary equations, global approximations are constructed. The lectures upon which this book is based were warmly received at the universities of Rome and Pavia, and at the Scuola Normale Superiore in Pisa. Here Professor Vishik has collated his lecture notes, and has added an appendix describing his work on attractors deriving from dynamical systems. This is unquestionably a fine addition to the Lezioni Lincee, and will be a necessary addition to the library of all who seek an insight into the solution of evolutionary equations.

Chapter

Cover

Half-title

Title

Copyright

Dedication

Contents

Introduction

Chapter I: Preliminaries

1 Attractors of evolutionary equations

2 Invariant manifolds

Chapter II: Local spectral asymptotics

3 Spectral asymptotics

4 Examples of local spectral asymptotics

Chapter III: Global spectral asymptotics

5 Global spectral asymptotics of trajectories

Chapter IV: Uniform approximation of trajectories of semigroups depending on a parameter

6 The principal asymptotic term

7 Stabilised asymptotics of solutions of reaction-diffusion systems, hyperbolic and parabolic equations

Chapter V: The asymptotics of solutions of reaction-diffusion equations with small parameter

8 Formulation of the problem

9 A priori estimates

10 The stabilised asymptotics of u(t)

Chapter VI: Asymptotics of elements lying on the attractor of solutions of the perturbed evolutionary equations

11 The main result

12 Construction of the asymptotic expansion

13 Proof of Theorem 12.1

14 Proof of Propositions 13.1 - 13.3

15 Problem with boundary conditions U\QQ =0, Au |aa= 0

Chapter VII: Asymptotics of solutions of singular perturbed evolutionary equations

16 Asymptotics of trajectories of the first boundary value problem

17 Global asymptotics of solutions of singular perturbed equation

Appendix: Non-autonomous dynamical systems and their attractors

Al Processes corresponding to non-autonomous equations and systems in mathematical physics

A2 Families of processes and their attractors: the general framework

A3 Attractors of families of processes generated by non-autonomous equations and systems in mathematical physics

A4 Upper bounds for the dimension of attractors of non-autonomous dynamic systems with quasi-periodic terms

A5 On finite-dimensionality of attractors of non-autonomous equations in mathematical physics with quasi-periodic terms

A6 Sections of attractors and their dimensionality; the case of almost periodic terms

References

The users who browse this book also browse


No browse record.