# 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

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 $K(x,y) = x^{\alpha }y^{\beta } + x^{\beta }y^{\alpha }$ and $a(x) = x^{\gamma }$, respectively, with $0 \leq \alpha \leq \beta \leq 1$, \alpha + \beta \in [0,1\right., and $\gamma > 0$. 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