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Asymptotic Behaviour of Solutions of Evolutionary Equationsby M. I. Vishik
Synopses & Reviews
The theme of this book is the investigation of globally asymptotic solutions of evolutionary equations, which are useful in the study of dynamical systems. The author begins with a construction of local asymptotics near the equilibrium points of Navier-Stokes equations, reaction-diffusion equations, and hyperbolic equations, which leads to a construction of global spectral asymptotics of solution of evolutionary equations, which are analogous to Fourier asymptotics in the linear case. He then deals with the global approximation of solutions of perturbed reaction diffusion equations, hyperbolic equations with dissipation, and parabolic systems. Finally, Dr. Vishik constructs the first asymptotic approximations of solution of singularly perturbed evolutionary equations.
A short but sweet summary of globally asymptotic solutions of evolutionary equations.
Table of Contents
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.
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