On the self-similar behavior of coagulation systems with injection
Marina A. Ferreira
University of Helsinki, FinlandEugenia Franco
University of Bonn, GermanyJuan J. L. Velázquez
University of Bonn, Germany
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Abstract
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 as , where is the homogeneity of the kernel, and are proven to decay at least exponentially as .
Cite this article
Marina A. Ferreira, Eugenia Franco, Juan J. L. Velázquez, On the self-similar behavior of coagulation systems with injection. Ann. Inst. H. Poincaré Anal. Non Linéaire 40 (2023), no. 4, pp. 803–861
DOI 10.4171/AIHPC/61