多组分混凝系统定常非平衡解的局部化
Localization in stationary non-equilibrium solutions for multicomponent coagulation systems
摘要：
我们认为多组分Smoluchowski凝聚方程的非平衡条件下诱导的源项或通过一个恒定的流量约束。我们证明了相应的定常非平衡解具有普适的局部化性质。更确切地说，我们表明，这些解决方案渐近本地化到由源或通量约束确定的方向：给定类型的单体之间的比率在集群中的单体的总数变得越来越接近一个预定的比率作为集群大小的增加。凝聚核的假设是相当普遍的，各向同性的幂律界限。证明依赖于一个特定的措施浓度估计和控制的渐近缩放的解决方案，这是允许由先前推导的估计系统的质量电流可观测的。
英文摘要：
We consider the multicomponent Smoluchowski coagulation equation under non-equilibrium conditions induced either by a source term or via a constant flux constraint. We prove that the corresponding stationary non-equilibrium solutions have a universal localization property. More precisely, we show that these solutions asymptotically localize into a direction determined by the source or by a flux constraint: the ratio between monomers of a given type to the total number of monomers in the cluster becomes ever closer to a predetermined ratio as the cluster size is increased. The assumptions on the coagulation kernel are quite general, with isotropic power law bounds. The proof relies on a particular measure concentration estimate and on the control of asymptotic scaling of the solutions which is allowed by previously derived estimates on the mass current observable of the system.
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