TY  - JOUR
A1  - Debussche, Arnaud
A1  - Högele, Michael
A1  - Imkeller, Peter
T1  - The Fine Dynamics of the Chafee-Infante Equation
T2  - Lecture notes in mathematics : a collection of informal reports and seminars
T2  - Lecture Notes in Mathematics
N2  - 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.
Y1  - 2013
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/35283
SN  - 978-3-319-00828-8; 978-3-319-00827-1
SN  - 0075-8434
VL  - 2085
SP  - 11
EP  - 43
PB  - Springer
CY  - Berlin
ER  -