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Bounded solutions for non-autonomous parabolic equations
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UNSPECIFIED (1996) Bounded solutions for non-autonomous parabolic equations. DYNAMICS AND STABILITY OF SYSTEMS, 11 (2). pp. 109-120. ISSN 0268-1110.
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Abstract
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 | ||||
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Subjects: | Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery |
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Journal or Publication Title: | DYNAMICS AND STABILITY OF SYSTEMS | ||||
Publisher: | CARFAX PUBL CO | ||||
ISSN: | 0268-1110 | ||||
Official Date: | June 1996 | ||||
Dates: |
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Volume: | 11 | ||||
Number: | 2 | ||||
Number of Pages: | 12 | ||||
Page Range: | pp. 109-120 | ||||
Publication Status: | Published |
Data sourced from Thomson Reuters' Web of Knowledge
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