Asymptotic Behaviour of Solutions of Evolutionary Equations

M. I. Vishik

doi:10.1017/CBO9780511608780

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.

"...makes a valuable contribution to the rich existing literature on the asymptotic behavior of solutions of nonlinear evolution equations." Piotr Biler, Mathematical Reviews

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Asymptotic Behaviour of Solutions of Evolutionary Equations

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Contents

Frontmatter
pp i-viii

Contents
pp ix-x

Introduction
pp 1-10

Chapter I - Preliminaries
pp 11-16

Chapter II - Local spectral asymptotics
pp 17-25

Chapter III - Global spectral asymptotics
pp 26-35

Chapter IV - Uniform approximation of trajectories of semigroups depending on a parameter
pp 36-51

Chapter V - The asymptotics of solutions of reaction-diffusion equations with small parameter
pp 52-68

Chapter VI - Asymptotics of elements lying on the attractor of solutions of the perturbed evolutionary equations
pp 69-96

Chapter VII - Asymptotics of solutions of singular perturbed evolutionary equations
pp 97-111

Appendix - Non-autonomous dynamical systems and their attractors
pp 112-150

References
pp 151-155

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