Uniqueness of fat-tailed self-similar profiles to Smoluchowski’s coagulation equation for a perturbation of the constant kernel
Uniqueness of fat-tailed self-similar profiles to Smoluchowski’s coagulation equation for a perturbation of the constant kernel
复制标题
肥尾自相似曲线与 Smoluchowski 凝固方程对常核扰动的唯一性
DOI：
10.1090/memo/1328
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发表时间：
2017
影响因子：
1.9
通讯作者：
S. Throm
中科院分区：
文献类型：
--
作者：
S. Throm
本文关注的是 Smoluchowski 凝固方程的自相似曲线的唯一性问题，该方程在无穷远处表现出代数衰减（厚尾）。更准确地说，我们考虑速率内核
K
K
可以写成
K
=
2
+
ε
瓦
K=2+\varepsilon W
。假设扰动的同质性为零，并且在零和无穷大处也可能是奇异的。在进一步的规律性假设下
瓦
瓦
，我们将证明对于足够小的
ε
瓦瑞普西隆
在无穷远处尾部行为归一化之前，至多存在一个自相似轮廓。
建立 Smoluchowski 凝固方程自相似曲线的唯一性通常被认为是一个难题，但本质上仍然是一个开放的问题。关于厚尾自相似轮廓，本文实际上给出了不可解核的第一个唯一性声明。
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
K
K
which can be written as
K
=
2
+
ε
W
K=2+\varepsilon W
. The perturbation is assumed to have homogeneity zero and might also be singular both at zero and at infinity. Under further regularity assumptions on
W
W
, we will show that for sufficiently small
ε
\varepsilon
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.
具有局部有界核的 Smoluchowski 凝固方程的厚尾自相似解
影响因子：
2.4
作者：
B. Niethammer;J. J. L. Veláquez
通讯作者：
J. J. L. Veláquez