Bounded solutions for non-autonomous parabolic equations
UNSPECIFIED (1996) Bounded solutions for non-autonomous parabolic equations. DYNAMICS AND STABILITY OF SYSTEMS, 11 (2). pp. 109-120. ISSN 0268-1110Full text not available from this repository.
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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
|Journal or Publication Title:||DYNAMICS AND STABILITY OF SYSTEMS|
|Publisher:||CARFAX PUBL CO|
|Number of Pages:||12|
|Page Range:||pp. 109-120|
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