Global Attractors and Robustness of the Boissonade System

In this work, the existence and properties of a global attractor for the weak solution semiflow of the Boissonade system are proved. A parameter adjusting and grouping estimation method is developed to show the absorbing property and asymptotic compactness of the solution trajectories of this reaction-diffusion system with quadratic and cubic nonlinearity. The upper-semicontinuity of the global attractors in the H1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^1$$\end{document} product space for the solution semiflow with respect to the quadratic term coefficient converging to zero is proved. The barrier of the perturbed singularity between zero quadratic term coefficient and non-zero one is overcome by the uniform adjusting parameter.