"This article is concerned with the question of uniqueness of self-similar profiles for Smoluchowski's coagulation equation which exhibit algebraic decay (fat tails) at infinity. More precisely, we consider a rate kernel which can be written as The perturbation is assumed to have homogeneity zero and might also be singular both at zero and at infinity. Under further regularity assumptions on we will show that for sufficiently small there exists, up to normalisation of the tail behaviour at infinity, at most one self-similar profile. Establishing uniqueness of self-similar profiles for Smoluchowski's coagulation equation is generally considered to be a difficult problem which is still essentially open. Concerning fat-tailed self-similar profiles this article actually gives the first uniqueness statement for a non-solvable kernel"--
Throm grapples with the question of uniqueness of self-similar profiles for Smoluchowski's coagulation equation that exhibit algebraic decay (fat tails) at infinity. More precisely, he considers a rate kernel K that can be written as K = 2 + eW. He assumes that the perturbation has homogeneity zero and might also be singular both at zero and at infinity. Under further regularlity assumptions on W, he shows that for sufficiently small e there exists--up to normalization of the tail behavior at infinity--at most one self-similar profile. Annotation ©2021 Ringgold, Inc., Portland, OR (protoview.com)
