We show that the Smoluchowski coagulation equation with the solvable kernels $K(x,y)$ equal to 2, $x+y$ or $xy$ is contractive in suitable Laplace norms. In particular, this proves exponential convergence to a self‐similar profile in these norms. These results are parallel to similar properties of Maxwell models for Boltzmann‐type equations, and extend already existing results on exponential convergence to self‐similarity for Smoluchowski's coagulation equation.

中文翻译：

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具有可解核的Smoluchowski凝聚方程的收缩性

我们证明了具有可解核的Smoluchowski凝聚方程 $ķ（X，ÿ）$ 等于2 $X+ÿ$ 要么 $Xÿ$在合适的拉普拉斯准则中具有收缩性。特别是，这证明了在这些规范中指数收敛到自相似轮廓。这些结果与Boltzmann型方程的麦克斯韦模型的相似性质平行，并将Smoluchowski凝聚方程的指数收敛性的已有结果扩展到自相似性。