Towards nonlinear stability of sources via a modified Burgers equation

PHYSICA D-NONLINEAR PHENOMENA

卷:241

Article

Beck, Margaret¹  Toan Nguyen²  Sandstede, Bjoern²  Zumbrun, Kevin³ 

[1] Boston Univ, Dept Math, Boston, MA 02215 USA

[2] Brown Univ, Div Appl Math, Providence, RI 02912 USA

[3] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

关键词: Defects;    Reaction-diffusion equations;    Pointwise estimates;    Nonlinear stability;   

DOI  :  10.1016/j.physd.2011.10.018

来源: Elsevier

【 摘 要 】

Coherent-structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at x = +/-infinity to spatially periodic travelling waves. This paper is concerned with sources which are coherent structures for which the group velocities in the far field point away from the core. Sources actively select wave numbers and therefore often organize the overall dynamics in a spatially extended system. Determining their nonlinear stability properties is challenging as localized perturbations may lead to a non-localized response even on the linear level due to the outward transport. Using a Burgers-type equation as a model problem that captures some of the essential features of sources, we show how this phenomenon can be analysed and asymptotic nonlinear stability be established in this simpler context. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free