论文标题
在多组分凝血系统的固定非平衡溶液中定位
Localization in stationary non-equilibrium solutions for multicomponent coagulation systems
论文作者
论文摘要
我们考虑通过源项或通过恒定通量约束诱导的非平衡条件下的多组分Smoluchowski凝结方程。我们证明相应的固定非平衡溶液具有通用定位属性。更确切地说，我们表明，这些溶液渐近地定位于由源或通量约束确定的方向：随着群集大小的增加，给定类型的单体与簇中的单体总数之间的比率越来越接近预定比率。对凝血核的假设非常笼统，以及各向同性幂律的界限。证明依赖于特定的度量浓度估计和控制溶液的渐近缩放量表的控制，这是通过对系统可观察到的质量电流的先前估计值允许的。
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.
