Geodesic
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

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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→∞.

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Publié le :
DOI : 10.4171/aihpc/61
Classification : 34A34, 45K05
Keywords: Self-similarity, Smoluchowski’s coagulation equation, constant flux solutions, source term, moment bounds 
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     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},
     volume = {40},
     number = {4},
     year = {2023},
     doi = {10.4171/aihpc/61},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/61/}
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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

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