no. 4
On the self-similar behavior of coagulation systems with injection
Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 4, pp. 803-861
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez l'article sur le site de la revue.

In this paper we prove the existence of a family of self-similar solutions for a class of coagulation equations with a constant flux of particles from the origin. These solutions are expected to describe the longtime asymptotics of Smoluchowski’s coagulation equations with a time-independent source of clusters concentrated in small sizes. The self-similar profiles are shown to be smooth, provided the coagulation kernel is also smooth. Moreover, the self-similar profiles are estimated from above and from below by x -(γ+3)/2 as x→0, where γ<1 is the homogeneity of the kernel, and are proven to decay at least exponentially as x→∞.

Accepté le :
Publié le :
DOI : 10.4171/aihpc/61
Classification : 34A34, 45K05
Keywords: Self-similarity, Smoluchowski’s coagulation equation, constant flux solutions, source term, moment bounds 
@article{AIHPC_2023__40_4_803_0,
     author = {Ferreira, Marina A. and Franco, Eugenia and Vel\'azquez, Juan J. L.},
     title = {On the self-similar behavior of coagulation systems with injection},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {803--861},
     year = {2023},
     volume = {40},
     number = {4},
     doi = {10.4171/aihpc/61},
     language = {en},
     url = {https://www.numdam.org/articles/10.4171/aihpc/61/}
}
TY  - JOUR
AU  - Ferreira, Marina A.
AU  - Franco, Eugenia
AU  - Velázquez, Juan J. L.
TI  - On the self-similar behavior of coagulation systems with injection
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2023
SP  - 803
EP  - 861
VL  - 40
IS  - 4
UR  - https://www.numdam.org/articles/10.4171/aihpc/61/
DO  - 10.4171/aihpc/61
LA  - en
ID  - AIHPC_2023__40_4_803_0
ER  - 
%0 Journal Article
%A Ferreira, Marina A.
%A Franco, Eugenia
%A Velázquez, Juan J. L.
%T On the self-similar behavior of coagulation systems with injection
%J Annales de l'I.H.P. Analyse non linéaire
%D 2023
%P 803-861
%V 40
%N 4
%U https://www.numdam.org/articles/10.4171/aihpc/61/
%R 10.4171/aihpc/61
%G en
%F AIHPC_2023__40_4_803_0
Ferreira, Marina A.; Franco, Eugenia; Velázquez, Juan J. L. On the self-similar behavior of coagulation systems with injection. Annales de l'I.H.P. Analyse non linéaire, Tome 40 (2023) no. 4, pp. 803-861. doi: 10.4171/aihpc/61

Cité par Sources :