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 SM ISO690:2012GRUNFELD, Cecil P.. On a positive semigroup associated to a nonlinear evolution model in an ordered space. In: Conference on Applied and Industrial Mathematics: CAIM 2022, Ed. 29, 25-27 august 2022, Chişinău. Chișinău, Republica Moldova: Casa Editorial-Poligrafică „Bons Offices”, 2022, Ediţia a 29, pp. 36-37. ISBN 978-9975-81-074-6. |
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| Conference on Applied and Industrial Mathematics Ediţia a 29, 2022 |
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Conferința "Conference on Applied and Industrial Mathematics" 29, Chişinău, Moldova, 25-27 august 2022 | ||||||
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| Pag. 36-37 | ||||||
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We re-examine the premises of a nonlinear evolution model in an abstract state space, in the sense of Davies, investigated in some recent works. We show that if the abstract state space is a Banach lattice, then the one-parameter C0 semigroup of positive linear operators, introduced by the assumptions of the model, is necessarily an (abstract) multiplication semigroup. The results are of interest, in particular, in the study of nonlinear kinetic equations, and example of applications to Boltzmann-like equations, Smoluchowski equation, etc, are provided. |
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