Banasiak, Jacek Transport processes with coagulation and strong fragmentation. (English) Zbl 1235.35275 Discrete Contin. Dyn. Syst., Ser. B 17, No. 2, 445-472 (2012). Summary: We deal with equations describing fragmentation and coagulation processes with growth or decay, where the latter are modelled by first order transport equations. Our main interest lies in processes with strong fragmentation and thus we carry out the analysis in spaces ensuring that higher moments of the solution exist. We prove that the linear part, consisting of the transport and fragmentation terms, generates a strongly continuous semigroup in such spaces and characterize its generator as the closure of the sum (and in some cases the sum itself) of the operators describing the transport and fragmentation, defined on their natural domains. These results allow us to prove the existence of global in time strict solutions to the full nonlinear fragmentation-coagulation-transport equation. Cited in 14 Documents MSC: 35Q92 PDEs in connection with biology, chemistry and other natural sciences 35A01 Existence problems for PDEs: global existence, local existence, non-existence 47D06 One-parameter semigroups and linear evolution equations Keywords:semigroups of operators; semilinear Cauchy problem; coagulation; fragmentation; transport processes; structured population models PDFBibTeX XMLCite \textit{J. Banasiak}, Discrete Contin. Dyn. Syst., Ser. B 17, No. 2, 445--472 (2012; Zbl 1235.35275) Full Text: DOI