Abstract
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.
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Debussche, A., Högele, M., Imkeller, P. (2013). The Fine Dynamics of the Chafee–Infante Equation. In: The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise. Lecture Notes in Mathematics, vol 2085. Springer, Cham. https://doi.org/10.1007/978-3-319-00828-8_2
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DOI: https://doi.org/10.1007/978-3-319-00828-8_2
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