Dynamical bifurcation for the Kuramoto-Sivashinsky equation

作者：Zhang, Yindi^*; Song, Lingyu; Axia, Wang

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(4): 1155-1163.

DOI：10.1016/j.na.2010.09.052

• Kuramoto-Sivashinsky equation
• Attractor bifurcation
• Eigenvalue analysis
• Center manifold

In this paper, by using the center manifold reduction method, together with the eigenvalue analysis, we made bifurcation analysis for the Kuramoto-Sivashinsky equation, and proved that the Kuramoto-Sivashinsky equation with constraint condition bifurcates an attractor A(lambda) as (lambda) crossed the first critical value lambda(0) = 1 under the two cases. Our analysis was based on a new and mature attractor bifurcation theory developed by Ma and Wang (2005) [17,18].

• 出版日期2011-2-15
• 单位西安交通大学; 长安大学