Stationary solutions to coagulation-fragmentation equations

2019/04/03 by Laurençot, Philippe
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1904.01868

Abstract

Existence of stationary solutions to the coagulation-fragmentation equation is shown when the coagulation kernel K and the overall fragmentation rate a are given by K(x, y) = x^αy^β+ x^βy^α and a(x) = x^γ, respectively, with 0≤ α≤ β≤1, α+β∈ [0, 1), and γ> 0. The proof requires two steps: a dynamical approach is first used to construct stationary solutions under the additional assumption that the coagulation kernel and the overall fragmentation rate are bounded from below by a positive constant. The general case is then handled by a compactness argument.

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