一类耦合二胞模型的全局吸引子
Global Attractor of a coupled Two-Cell Brusselator Model
摘要：
本文证明了耦合二胞模型方程解半流的全局吸引子的存在性。针对这类具有三次自催化非线性和线性耦合的四变量反应扩散系统的吸收性和渐近紧性的证明问题，提出了一种分组估计方法和一种新的分解方法.证明了全局吸引子的豪斯多夫维数和分形维数是有限的。
英文摘要：
In this work the existence of a global attractor for the solution semiflow of the coupled two-cell Brusselator model equations is proved. A grouping estimation method and a new decomposition approach are introduced to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of four-variable reaction-diffusion systems with cubic autocatalytic nonlinearity and with linear coupling. It is also proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite.
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