The Fine Dynamics of the Chafee-Infante Equation
- In this chapter, we introduce the deterministic Chafee-Infante equation. This equation has been the subject of intense research and is very well understood now. We recall some properties of its longtime dynamics and in particular the structure of its attractor. We then define reduced domains of attraction that will be fundamental in our study and give a result describing precisely the time that a solution starting form a reduced domain of attraction needs to reach a stable equilibrium. This result is then proved using the detailed knowledge of the attractor and classical tools such as the stable and unstable manifolds in a neighborhood of an equilibrium.
| Author details: | Arnaud Debussche, Michael HögeleGND, Peter Imkeller |
|---|---|
| DOI: | https://doi.org/10.1007/978-3-319-00828-8_2 |
| ISBN: | 978-3-319-00828-8; 978-3-319-00827-1 |
| ISSN: | 0075-8434 |
| Title of parent work (English): | Lecture notes in mathematics : a collection of informal reports and seminars |
| Title of parent work (English): | Lecture Notes in Mathematics |
| Publisher: | Springer |
| Place of publishing: | Berlin |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2013 |
| Publication year: | 2013 |
| Release date: | 2017/03/26 |
| Volume: | 2085 |
| Number of pages: | 33 |
| First page: | 11 |
| Last Page: | 43 |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
