| Автор | Zhang, Weinian |
| Автор | Stewart, Ian |
| Дата выпуска | 1996 |
| dc.description | 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 |
| Формат | application.pdf |
| Издатель | Journals Oxford Ltd |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Название | Bounded solutions for non-autonomous parabolic equations |
| Тип | research-article |
| DOI | 10.1080/02681119608806219 |
| Electronic ISSN | 1465-3389 |
| Print ISSN | 0268-1110 |
| Журнал | Dynamics and Stability of Systems |
| Том | 11 |
| Первая страница | 109 |
| Последняя страница | 120 |
| Аффилиация | Zhang, Weinian; Centre for Mathematical Sciences, CICA, Academia Sinica |
| Аффилиация | Stewart, Ian; Mathematics Institute, University of Warwick |
| Выпуск | 2 |
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