1111.6379 (Barbara Niethammer et al.)

Self-similar solutions with fat tails for Smoluchowski's coagulation
equation with locally bounded kernels    [PDF]

Barbara Niethammer, Juan J. L. Velazquez

The existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation has so far only been established for the solvable and the diagonal kernel. In this paper we prove the existence of such self-similar solutions for continuous kernels $K$ that are homogeneous of degree $\gamma \in (-\infty,1)$ and satisfy $K(x,y) \leq C (x^{\gamma} + y^{\gamma})$. More precisely, for any $\rho \in (\gamma,1)$ we establish the existence of a continuous weak self-similar profile with decay $x^{-(1{+}\rho)}$ as $x \to \infty$.

View original: http://arxiv.org/abs/1111.6379