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 t
Asymptotics for Dissipative Nonlinear Equations
β Scribed by Nakao Hayashi, Pavel I. Naumkin, Elena I. Kaikina, Ilya A. Shishmarev (auth.)
- Book ID
- 127448529
- Publisher
- Springer
- Year
- 2006
- Tongue
- English
- Weight
- 6 MB
- Edition
- 1
- Category
- Library
- City
- Berlin; New York
- ISBN
- 3540320601
- ISSN
- 0075-8434
- DOI
- 10.1007/b133345
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β¦ Synopsis
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.
β¦ Subjects
Mathematical and Computational Physics
π SIMILAR VOLUMES
## Abstract We study the Cauchy problem of nonlinear KleinβGordon equation with dissipative term. By introducing a family of potential wells, we derive the invariant sets and prove the global existence, finite time blow up as well as the asymptotic behaviour of solutions. In particular, we show a s