Self-similar solutions with fat tails for a coagulation equation with\n diagonal kernel

2011/03/15 by Barbara Niethammer, Niethammer, Barbara, Juan Juan J. L. Velázquez +1
Computer Science · Mathematics · Medicine · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1103.2868

openalex publication_date 2011/03/15 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We consider self-similar solutions of Smoluchowski's coagulation equation\nwith a diagonal kernel of homogeneity \γ < 1. We show that there exists a\nfamily of second-kind self-similar solutions with power-law behavior\nx^-(1+\ρ) as x \→ \∞ with \ρ \∈ (\γ,1). To our knowledge\nthis is the first example of a non-solvable kernel for which the existence of\nsuch a family has been established.\n

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