Stationary solutions to coagulation-fragmentation equations

Laurençot, Philippe

doi:10.1016/j.anihpc.2019.06.003

Laurençot, Philippe

Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 7, pp. 1903-1939.

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Résumé

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 $K (x, y) = x^{α} y^{β} + x^{β} y^{α}$ and $a (x) = x^{γ}$ , respectively, with $0 \leq α \leq β \leq 1$ , $α + β \in [0, 1)$ , 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.

MR Zbl

DOI : 10.1016/j.anihpc.2019.06.003

Classification : 45K05, 45M99
Mots-clés : Coagulation, Fragmentation, Stationary solution, Mass conservation

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     title = {Stationary solutions to coagulation-fragmentation equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
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Laurençot, Philippe. Stationary solutions to coagulation-fragmentation equations. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 7, pp. 1903-1939. doi : 10.1016/j.anihpc.2019.06.003. http://archive.numdam.org/articles/10.1016/j.anihpc.2019.06.003/

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