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Remarks on the Kuramoto-Sivashinsky equation. (English) Zbl 0576.35058

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.

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
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References:

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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.