标题： Smoluchowski凝聚方程的质量守恒与凝胶化：广义矩方法 显示英文标题

标题： Mass conservation and gelation for the Smoluchowski coagulation equation: a generalized moment approach

摘要： Smoluchowski凝聚方程（SCE）是一种群体平衡模型，描述了由颗粒聚集引起的聚集体尺寸分布随时间的演化。 尽管从形式上看它是一个质量守恒系统，但当凝聚核以超线性增长时，解可能会表现出胶凝现象——即突然的质量损失。 本文严格分析了具有非均匀凝聚核的SCE弱解的质量守恒和胶凝现象。 通过引入广义矩框架，我们推导出关于初始数据和凝聚核性质的、用于质量守恒和胶凝的精确充分条件。 显示英文摘要

摘要： The Smoluchowski coagulation equation (SCE) is a population balance model that describes the time evolution of cluster size distributions resulting from particle aggregation. Although it is formally a mass-conserving system, solutions may exhibit a gelation phenomenon-a sudden loss of mass-when the coagulation kernel grows superlinearly. In this paper, we rigorously analyze mass conservation and gelation for weak solutions to the SCE with inhomogeneous coagulation kernels. By introducing a generalized moment framework, we derive sharp sufficient conditions for both mass conservation and gelation, expressed in terms of the initial data and the properties of the coagulation kernel.