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https://hdl.handle.net/10316/111216
Title: | Long-time asymptotics for coagulation equations with injection that do not have stationary solutions | Authors: | Cristian, Iulia Ferreira, Marina A. Franco, Eugenia Velázquez, Juan J. L. |
Issue Date: | 2023 | Publisher: | Springer Nature | Project: | UIDB/00324/2020 | Serial title, monograph or event: | Archive for Rational Mechanics and Analysis | Volume: | 247 | Issue: | 6 | Abstract: | In this paper we study a class of coagulation equations including a source term that injects in the system clusters of size of order one. The coagulation kernel is homogeneous, of homogeneityγ < 1, such that K(x, y) is approximately xγ+λ y−λ, when x is larger than y. We restrict the analysis to the case γ + 2λ ≥ 1. In this range of exponents, the transport of mass toward infinity is driven by collisions between particles of different sizes. This is in contrast with the case considered in Ferreira et al. (Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire, 2023), where γ +2λ < 1. In that case, the transport of mass toward infinity is due to the collision between particles of comparable sizes. In the case γ + 2λ ≥ 1, the interaction between particles of different sizes leads to an additional transport term in the coagulation equation that approximates the solution of the original coagulation equation with injection for large times.We prove the existence of a class of self-similar solutions for suitable choices of γ and λ for this class of coagulation equations with transport. We prove that for the complementary case such self-similar solutions do not exist. | URI: | https://hdl.handle.net/10316/111216 | ISSN: | 0003-9527 1432-0673 |
DOI: | 10.1007/s00205-023-01934-0 | Rights: | openAccess |
Appears in Collections: | FCTUC Matemática - Artigos em Revistas Internacionais |
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