Geodesic
Self-similar gelling solutions for the coagulation equation with diagonal kernel
Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 3, pp. 705-744

Voir la notice de l'article provenant de la source Numdam

We consider Smoluchowski's coagulation equation in the case of the diagonal kernel with homogeneity γ>1. In this case the phenomenon of gelation occurs and solutions lose mass at some finite time. The problem of the existence of self-similar solutions involves a free parameter b, and one expects that a physically relevant solution (i.e. nonnegative and with sufficiently fast decay at infinity) exists for a single value of b, depending on the homogeneity γ. We prove this picture rigorously for large values of γ. In the general case, we discuss in detail the behavior of solutions to the self-similar equation as the parameter b changes.

DOI : 10.1016/j.anihpc.2018.09.001
Keywords: Smoluchowski's coagulation equation, Self-similar solutions, Gelation 
@article{AIHPC_2019__36_3_705_0,
     author = {Bonacini, Marco and Niethammer, Barbara and Vel\'azquez, Juan J.L.},
     title = {Self-similar gelling solutions for the coagulation equation with diagonal kernel},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {705--744},
     publisher = {Elsevier},
     volume = {36},
     number = {3},
     year = {2019},
     doi = {10.1016/j.anihpc.2018.09.001},
     zbl = {1412.82032},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.09.001/}
}
TY  - JOUR
AU  - Bonacini, Marco
AU  - Niethammer, Barbara
AU  - Velázquez, Juan J.L.
TI  - Self-similar gelling solutions for the coagulation equation with diagonal kernel
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2019
SP  - 705
EP  - 744
VL  - 36
IS  - 3
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.09.001/
DO  - 10.1016/j.anihpc.2018.09.001
LA  - en
ID  - AIHPC_2019__36_3_705_0
ER  - 
%0 Journal Article
%A Bonacini, Marco
%A Niethammer, Barbara
%A Velázquez, Juan J.L.
%T Self-similar gelling solutions for the coagulation equation with diagonal kernel
%J Annales de l'I.H.P. Analyse non linéaire
%D 2019
%P 705-744
%V 36
%N 3
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.09.001/
%R 10.1016/j.anihpc.2018.09.001
%G en
%F AIHPC_2019__36_3_705_0
Bonacini, Marco; Niethammer, Barbara; Velázquez, Juan J.L. Self-similar gelling solutions for the coagulation equation with diagonal kernel. Annales de l'I.H.P. Analyse non linéaire, Tome 36 (2019) no. 3, pp. 705-744. doi: 10.1016/j.anihpc.2018.09.001

Cité par Sources :