25,536 research outputs found
Self-similar solutions with fat tails for a coagulation equation with diagonal kernel
We consider self-similar solutions of Smoluchowski's coagulation equation
with a diagonal kernel of homogeneity . We show that there exists a
family of second-kind self-similar solutions with power-law behavior
as with . To our knowledge
this is the first example of a non-solvable kernel for which the existence of
such a family has been established
Optimal bounds for self-similar solutions to coagulation equations with product kernel
We consider mass-conserving self-similar solutions of Smoluchowski's
coagulation equation with multiplicative kernel of homogeneity . We establish rigorously that such solutions exhibit a singular behavior
of the form as . This property had been
conjectured, but only weaker results had been available up to now
- …