Asymptotics for Dissipative Nonlinear Equations

Nakao Hayashi, Pavel I. Naumkin, Elena I. Kaikina, Ilya A. Shishmarev (auth.)9783540320593, 3-540-32059-8

Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.

Table of contents :
Preliminary results….Pages 1-50
Weak Nonlinearity….Pages 51-178
Critical Nonconvective Equations….Pages 179-322
Critical Convective Equations….Pages 323-429
Subcritical Nonconvective Equations….Pages 431-512
Subcritical Convective Equations….Pages 513-540