Nicolaenko, Basil; Scheurer, Bruno Remarks on the Kuramoto-Sivashinsky equation. (English) Zbl 0576.35058 Physica D 12, 391-395 (1984). Summary: We report some preliminary results on the Kuramoto-Sivashinsky equation which models instabilities for both flame front cellular patterns and chemical reaction-diffusion waves. We present existence and uniqueness results and a fraction step method of numerical resolution. Cited in 30 Documents MSC: 35K55 Nonlinear parabolic equations 35Q99 Partial differential equations of mathematical physics and other areas of application 35B35 Stability in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs Keywords:fourth order nonlinear evolution equation; Kuramoto-Sivashinsky equation; instabilities; flame front cellular patterns; chemical reaction-diffusion waves; existence; uniqueness; fraction step method PDFBibTeX XMLCite \textit{B. Nicolaenko} and \textit{B. Scheurer}, Physica D 12, 391--395 (1984; Zbl 0576.35058) Full Text: DOI Link References: [1] Adams, A., Sobolev Spaces (1979), Academic Press: Academic Press New York [2] Aimar, M. T., Thèse 3° Cycle (1982) [3] Kuramoto, Y., Prog. of Theor. Phys., 63, 1885-1903 (1980) · Zbl 1059.80503 [4] Lions, J. L.; Magenes, E., Problèmes aux limites non homogenes (1968), Dunod: Dunod Paris · Zbl 0165.10801 [5] P. Manneville, unpublished.; P. Manneville, unpublished. [6] Michelson, D.; Sivashinsky, G. I., Acta Astronautica, 4, 1207-1221 (1977) [7] J.M. Hyman, private communication.; J.M. Hyman, private communication. [8] Sivashinsky, G. I., Acta Astronautica, 4, 1117-1206 (1977) [9] Foias, C.; Manley, O.; Temam, R.; Treve, Y., Physica, 9D, 157 (1983) 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.