Local properties of self-similar solutions to Smoluchowski’s coagulation equation with sum kernels
Local properties of self-similar solutions to Smoluchowski’s coagulation equation with sum kernels
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带和核的 Smoluchowski 凝固方程自相似解的局部性质
DOI：
10.1017/s0308210500005035
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
P. Laurençot
中科院分区：
文献类型：
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作者：
N. Fournier;P. Laurençot
研究了当凝聚核K为K(x，y)=xψ+yλ且λ为λ∈(0，1)时，Smoluchowski凝聚方程标度分布的规律性。更准确地说，ψ在(0，∞)上是C_1-光滑的，并且当x较大时，ψ(X)的衰减速度是指数快的。此外，还证明了→(X)在x_→_0时的奇异行为，从而给出了物理猜想的严格证明。
The regularity of the scaling profiles ψ to Smoluchowski’s coagulation equation is studied when the coagulation kernel K is given by K(x, y) = xλ + yλ with λ∈ (0, 1). More precisely, ψ is C1-smooth on (0,∞) and decays exponentially fast for large x. Furthermore, the singular behaviour of ψ(x) as x → 0 is identified, thus giving a rigorous proof of physical conjectures.