GLOBAL SOLUTIONS AND EXPONENTIAL ATTRACTORS OF A PARABOLIC-PARABOLIC SYSTEM FOR CHEMOTAXIS WITH SUBQUADRATIC DEGRADATION
GLOBAL SOLUTIONS AND EXPONENTIAL ATTRACTORS OF A PARABOLIC-PARABOLIC SYSTEM FOR CHEMOTAXIS WITH SUBQUADRATIC DEGRADATION
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DOI：
10.3934/dcdsb.2013.18.2627
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发表时间：
2013-10
影响因子：
1.2
通讯作者：
E. Nakaguchi;Koichi Osaki
中科院分区：
文献类型：
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作者：
E. Nakaguchi;Koichi Osaki
我们在二维和三维光滑有界域中构建了抛物线-抛物线趋化生长系统的全局有界解和吸引子。我们对这些解决方案得出新的 $L_p$ 和 $H^2$ 统一估计。然后，我们为解生成的动力系统构建吸收集和全局吸引子。我们还通过应用 Eden-Foias-Nicolaenko-Temam 存在定理证明了指数吸引子的存在性。
We construct the global bounded solutions and the attractors of a parabolic-parabolic chemotaxis-growth system in two- and three-dimensional smooth bounded domains. We derive new $L_p$ and $H^2$ uniform estimates for these solutions. We then construct the absorbing sets and the global attractors for the dynamical systems generated by the solutions. We also show the existence of exponential attractors by applying the existence theorem of Eden-Foias-Nicolaenko-Temam.