Generalization of the reaction-diffusion, the Swift-Hohenberg and the Kuramoto-Sivashinsky equation and effects of finite propagation speeds

Details Generalization of the reaction-diffusion, the Swift-Hohenberg and the Kuramoto-Sivashinsky equation and effects of finite propagation speeds Generalization of the reaction-diffusion, the Swift-Hohenberg and the Kuramoto-Sivashinsky equation and effects of finite propagation speeds

2006-10-04

arxiv.org/abs/cond-mat/0610125v3

Physics

Condensed Matter

Other Condensed Matter

20 pages, 6 figures

Scientific paper

The work proposes and studies a one-dimensional model, which involves nonlocal interactions and finite propagation speed. It shows that the general reaction-diffusion equation, the Swift-Hohenberg equation and the general Kuramoto-Sivashinsky equation represent special cases of the proposed model for limited spatial interaction ranges and for infinite propagation speeds. After a detailed validity study on the generalization conditions, the three equations are extended to involve finite propagation speeds. Moreover linear stability studies of the extended equations reveal critical propagation speeds and novel types of instabilities in all three equations. In addition, an extended diffusion equation is derived and studied in some detail with respect to finite propagation speeds. The extended model allows for the explanation of recent experimental results on non-Fourier heat conduction in non-homogeneous material.

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