A revised proof of uniqueness of self-similar profiles to Smoluchowski's\n coagulation equation for kernels close to constant

2015/10/12 by Barbara Niethammer, Niethammer, Barbara, Sebastian Throm +3
Mathematics · Computer Science · #Stochastic processes and statistical mechanics #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1510.03361

Abstract

In this article we correct the proof of a uniqueness result for self-similar\nsolutions to Smoluchowski's coagulation equation for kernels K=K(x,y) that\nare homogeneous of degree zero and close to constant in the sense that\n n -
varepsilon
leq K(x,y)-2
leq
varepsilon
left(\n
Big(
fracxy
Big)
^alpha +
Big(
fracyx
Big)
^alpha
right)\n for \α \∈ [0, frac 1 2). Assuming in addition that K\nhas an analytic extension to \ℂ\∖(-\∞,0] and prescribing\nthe precise asymptotic behaviour of K at the origin, we prove that\nself-similar solutions with given mass are unique if \ε is\nsufficiently small.\n

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