Asymptotic Behaviour of Solutions of Evolutionary Equations

A short but sweet summary of globally asymptotic solutions of evolutionary equations.

M. I. Vishik (Author)

9780521420235, Cambridge University Press

Hardback, published 28 January 1993

168 pages
22.4 x 14.6 x 1.6 cm, 0.332 kg

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

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.

1. Preliminaries
2. Local spectral asymptotics
3. Global spectral asymptotics
4. Uniform approximation of trajectories of solutions of semigroups depending on a parameter
5. The asymptotics of solutions of reaction diffusion equations with small parameter
6. Asymptotics of elements lying on the attractor of solutions of the perturbed evolutionary equations
7. Asymptotics of solutions of singular perturbed evolutionary equations
Appendix.

Subject Areas: Differential calculus & equations [PBKJ]