\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

On a Burgers' type equation

Abstract / Introduction Related Papers Cited by
  • In this paper we study the dynamics of a Burgers' type equation (1). First, we use a new method called attractor bifurcation introduced by Ma and Wang in [4, 6] to study the bifurcation of Burgers' type equation out of the trivial solution. For Dirichlet boundary condition, we get pitchfork attrac- tor bifurcation as the parameter $\lambda$ crosses the first eigenvalue. For periodic boundary condition, we get bifurcated $S^{1}$ attractor consisting of steady states. Second, we study the long time behavior of the equation. We show that there exists a global attractor whose dimension is at least of the order of $\sqrt{\lambda}$. Thus it provides another example of extended system (see (2)) whose global attractor has a Hausdorff/fractal dimension that scales at least linearly in the system size while the long time dynamics is non-chaotic.
    Mathematics Subject Classification: Primary: 37G35, 35B32; Secondary: 35B40.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(94) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return