扩展的自振子系统的全局耗散动力学
Global Dissipative Dynamics of the Extended Brusselator System
摘要：
证明了在$L^2$相空间中推广的自催化部分可逆反应扩散系统解半流的全局吸引子的存在性.针对这类典型的多组分反应扩散方程组的吸收性和渐近紧性的证明问题，提出了分组重标度估计方法。证明了该全局吸引子是具有$L^\infty$正则性的$(H, E)$全局吸引子，并且该全局吸引子的豪斯多夫维数和分形维数是有限的.这些结果和方法在复杂的生物和生化动力系统中有着广泛的应用和进一步的推广。
英文摘要：
The existence of a global attractor for the solution semiflow of the extended Brusselator system in the $L^2$ phase space is proved, which is a cubic-autocatalytic and partially reversible reaction-diffusion system with linear coupling between two compartments. The method of grouping and re-scaling estimation is developed to deal with the challenge in proving the absorbing property and the asymptotic compactness of this typical multi-component reaction-diffusion systems. It is also proved that the global attractor is an $(H, E)$ global attractor with the $L^\infty$ regularity and that the Hausdorff dimension and the fractal dimension of the global attractor are finite. The results and methodology can find many applications and further extensions in complex biological and biochemical dynamical systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
