Influence of obstacles on the propagation speeds of nonlinear waves driven by curvature

Cheng Wang, Jiale Tan and Bendong Lou

Physica A: Statistical Mechanics and its Applications, 2015, vol. 425, issue C, 41-49

Abstract: We consider nonlinear waves driven by curvature in the presence of periodically distributed obstacles. When the obstacles are small, Matano et al. (2006) proved rigorously that the propagation speed of a wave mainly depends on the opening angle of the obstacles. In this paper we first explain in a formal way that, when the obstacles are small, the propagation behavior of a wave near the obstacles has four different stages in one spatial period, they can be described by traveling waves, self-similar solutions, or curvature flows without driving force. When the obstacles are large, by numerical simulation we show that obstacles always decrease the propagation of waves; the propagation speed is decreasing in the opening angles and the sizes of the obstacles; but it is not monotone in the homogenization degree of the obstacles, the periods of obstacles in a row, or the isthmus widths between two rows.

Keywords: Nonlinear waves driven by curvature; Propagation speed; Obstacle; Numerical simulation (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:425:y:2015:i:c:p:41-49

DOI: 10.1016/j.physa.2015.01.046

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