A new mode reduction strategy for the generalized Kuramoto-Sivashinsky equation

作者：Schmuck M; Pradas M; Pavliotis G A; Kalliadasis S^*

来源：IMA Journal of Applied Mathematics, 2015, 80(2): 273-301.

DOI：10.1093/imamat/hxt041

• generalized Kuramoto-Sivashinsky equation
• renormalization group method
• stochastic mode reduction

Consider the generalized Kuramoto-Sivashinsky (gKS) equation. It is a model prototype for a wide variety of physical systems, from flame-front propagation, and more general front propagation in reaction-diffusion systems, to interface motion of viscous film flows. Our aim is to develop a systematic and rigorous low-dimensional representation of the gKS equation. For this purpose, we approximate it by a renormalization group equation which is qualitatively characterized by rigorous error bounds. This formulation allows for a new stochastic mode reduction guaranteeing optimality in the sense of maximal information entropy. Herewith, noise is systematically added to the reduced gKS equation and gives a rigorous and analytical explanation for its origin. These new results would allow one to reliably perform low-dimensional numerical computations by accounting for the neglected degrees of freedom in a systematic way. Moreover, the presented reduction strategy might also be useful in other applications where classical mode reduction approaches fail or are too complicated to be implemented.

• 出版日期2015-4