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| Titel: |
Bounded solutions for non-autonomous parabolic equations |
| Auteur: |
Zhang, Weinian Stewart, Ian |
| Verschenen in: |
Dynamical systems |
| Paginering: | Jaargang 11 (1996) nr. 2 pagina's 109-120 |
| Jaar: |
1996 |
| Inhoud: |
The existence of bounded solutions (including in particular homoclinic and heteroclinic solutions) is studied for non-autonomous perturbed parabolic partial differential equations, without the restriction that the linear variational equation has a unique non-trivial bounded solution. Specifically, an idea applied to ordinary differential equations by Hale (1984) and by Battelli and Laari (1990) is realised in an infinite-dimensional setting. Like other work on related problems, the main technique is Lyapunov?Schmidt reduction; we use that technique here in the context of bounded solutions, rather than the more usual setting of periodic or homoclinic solutions. Moreover, several technical obstacles are circumvented in the infinite-dimensional setting?in particular in the proof of the existence of a solution to the reduced bifurcation equation. Non-uniqueness is shown to occur for the Kuramoto-Sivashinsky equation, demonstrating the need to remove the uniqueness restriction |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 2 van 5 gevonden artikelen
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