论文标题
非球形簇的凝结方程
Coagulation equations for non-spherical clusters
论文作者
论文摘要
在这项工作中，我们研究了凝血模型的长时间渐近学，该模型描述了以其体积和表面积为特征的颗粒系统的演变。聚集机制分为两个阶段：粒子的碰撞和融合。在碰撞阶段，两个粒子在接触点合并。新形成的粒子的体积和面积等于两个碰撞颗粒的相应数量的总和。碰撞后，融合阶段开始，在其期间，相互作用粒子的几何形状被修改，以至于保留了总系统的体积并减少了表面积。在它们的进化过程中，颗粒必须满足等等不等式。因此，在$ \ {a \ geq（36π）^{\ frac {1} {3}} v^{\ frac {\ frac {2} {3} {3} {3}} \} $的区域中支持粒子的分布。我们假设凝血核对面积变量的依赖性较弱。我们证明存在自相似曲线的存在，用于描述粒子具有接近球形的融合速率的功能的某些选择。另一方面，对于其他融合机制和适当的初始数据选择，我们表明粒子分布描述了一种类似分支的粒子系统。
In this work, we study the long time asymptotics of a coagulation model which describes the evolution of a system of particles characterized by their volume and surface area. The aggregation mechanism takes place in two stages: collision and fusion of particles. During the collision stage, the two particles merge at a contact point. The newly formed particle has volume and area equal to the sum of the respective quantities of the two colliding particles. After collision, the fusion phase begins and during it the geometry of the interacting particles is modified in such a way that the volume of the total system is preserved and the surface area is reduced. During their evolution, the particles must satisfy the isoperimetric inequality. Therefore, the distribution of particles in the volume and area space is supported in the region where $\{a\geq (36π)^{\frac{1}{3}}v^{\frac{2}{3}}\}$. We assume the coagulation kernel has a weak dependence on the area variable. We prove existence of self-similar profiles for some choices of the functions describing the fusion rate for which the particles have a shape that is close to spherical. On the other hand, for other fusion mechanisms and suitable choices of initial data, we show that the particle distribution describes a system of ramified-like particles.
