×
Chen, Wenhan

Low dimensional approximate inertial manifolds for the Kuramoto- Sivashinsky equation. (English) Zbl 0792.35072

Numer. Funct. Anal. Optimization 14, No. 3-4, 265-274 (1993).
Summary: We first modify the Kuramoto-Sivashinsky equation (KSE) by broadening the gaps between some two successive eigenvalues over a narrow band which corresponds to low modes of the dissipative operator so that the resulting equations possess low dimensional inertial manifolds. We then prove these manifolds approximate the inertial manifold of the KSE and thus can be regarded as approximate inertial manifolds for the KSE.

MSC:

35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K35 Initial-boundary value problems for higher-order parabolic equations

Keywords:

spectral barrier; Kuramoto-Sivashinsky equation; low dimensional inertial manifolds; approximate inertial manifolds
Cite Review PDF
Full Text: DOI

References:

[1] Chen W., J. Math. Anal & Appl. 165 pp 399– · Zbl 0809.35072 · doi:10.1016/0022-247X(92)90048-I
[2] DOI: 10.1007/BF01048790 · Zbl 0701.35024 · doi:10.1007/BF01048790
[3] Constantin P., Mem. Amer. Math. Soc. 53 (1985)
[4] Fabes E., IMA 459 (1988)
[5] Foias C., Math. Mod. and Num. Anal. 22 pp 93– (1988)
[6] Foias C., J. Math. Pures Appl. 67 pp 309– (1988)
[7] DOI: 10.1016/0022-0396(88)90110-6 · Zbl 0643.58004 · doi:10.1016/0022-0396(88)90110-6
[8] DOI: 10.1007/BF01047831 · Zbl 0692.35053 · doi:10.1007/BF01047831
[9] Foias C., C. R. Acad.Sci. Paris 307 pp 67– (1988)
[10] DOI: 10.1016/0167-2789(90)90046-R · Zbl 0704.58030 · doi:10.1016/0167-2789(90)90046-R
[11] DOI: 10.1090/S0894-0347-1988-0943276-7 · doi:10.1090/S0894-0347-1988-0943276-7
[12] Marion M., Math. Mod. Num. Anal 23 pp 463– (1989)
[13] DOI: 10.1016/0167-2789(85)90056-9 · Zbl 0592.35013 · doi:10.1016/0167-2789(85)90056-9
[14] Temam R., Math. Modelling Num. Anal. 23 pp 541– (1989)
[15] DOI: 10.1016/0022-247X(90)90061-J · Zbl 0723.35063 · doi:10.1016/0022-247X(90)90061-J
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.