Spatial complexity of solutions of higher order partial differential equations
In: Nonlinearity, Jg. 17 (2003-12-01), S. 459-476
Online
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Zugriff:
We address spatial oscillation properties of solutions of higher order parabolic partial differential equations. In the case of the Kuramoto–Sivashinsky equation ut + uxxxx + uxx + u ux = 0, we prove that for solutions u on the global attractor, the quantity card {x [0, L]:u(x, t) = λ}, where L > 0 is the spatial period, can be bounded by a polynomial function of L for all . A similar property is proven for a general higher order partial differential equation .
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Spatial complexity of solutions of higher order partial differential equations
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Autor/in / Beteiligte Person: | Kukavica, Igor |
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Zeitschrift: | Nonlinearity, Jg. 17 (2003-12-01), S. 459-476 |
Veröffentlichung: | IOP Publishing, 2003 |
Medientyp: | unknown |
ISSN: | 1361-6544 (print) ; 0951-7715 (print) |
DOI: | 10.1088/0951-7715/17/2/005 |
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