消散非線形方程式の漸近理論 Asymptotics for Dissipative Nonlinear Equations (Lecture Notes in Mathematics) 〈Vol. 1884〉

Hayashi, Nakao/ Kaikina, Elena I./ Naumkin, Pavel I. (et al.)

Springer（2006/04発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 557 p.
• 商品コード 9783540320593

Full Description

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.

Contents

Preliminary results.- Weak Nonlinearity.- Critical Nonconvective Equations.- Critical Convective Equations.- Subcritical Nonconvective Equations.- Subcritical Convective Equations.