Spatial complexity of solutions of higher order partial differential equations
In: Nonlinearity (Bristol. Print), Jg. 17 (2004), Heft 2, S. 459-476
Online
academicJournal
- print, 28 ref
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 + uux = 0, we prove that for solutions u on the global attractor, the quantity card{x E [0, L] : u(x,t) = λ}, where L > 0 is the spatial period, can be bounded by a polynomial function of L for all λ E R. A similar property is proven for a general higher order partial differential equation ut + (-1)s∂2sxu + Σ2s-1k=0 vk(x, t)∂kxu = 0.
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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 (Bristol. Print), Jg. 17 (2004), Heft 2, S. 459-476 |
Veröffentlichung: | Bristol: Institute of Physics, 2004 |
Medientyp: | academicJournal |
Umfang: | print, 28 ref |
ISSN: | 0951-7715 (print) |
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