JournalsaihpcVol. 36, No. 7pp. 1903–1939

Stationary solutions to coagulation-fragmentation equations

  • Philippe Laurençot

    Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, F-31062 Toulouse Cedex 9, France
Stationary solutions to coagulation-fragmentation equations cover
Download PDF

A subscription is required to access this article.

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)=xαyβ+xβyαK(x,y) = x^{\alpha }y^{\beta } + x^{\beta }y^{\alpha } and a(x)=xγa(x) = x^{\gamma }, respectively, with 0αβ10 \leq \alpha \leq \beta \leq 1, \alpha + \beta \in [0,1\right., and γ>0\gamma > 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.

Cite this article

Philippe Laurençot, Stationary solutions to coagulation-fragmentation equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 7, pp. 1903–1939

DOI 10.1016/J.ANIHPC.2019.06.003