2019/02/12 by Jacek Banasiak, Banasiak, Jacek
Mathematics · #47D06 #47J35 #82C05 #82C22 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35R09 #Secondary: 35K58 #math.AP #msc:35K58 #msc:35R09 #msc:47D06 #msc:47J35 #msc:82C05 #msc:82C22
paper · pdf · doi:10.48550/arxiv.1902.04452
16 pages
arxiv created 2019/02/12 · arxiv updated 2019/02/13
In this paper we prove the existence of global classical solutions to continuous coagulation-fragmentation equations with unbounded coefficients under the sole assumption that the coagulation rate is dominated by a power of the fragmentation rate, thus improving upon a number of recent results by not requiring any polynomial growth bound for either rate. This is achieved by proving a new result on the analyticity of the fragmentation semigroup and then using its regularizing properties to prove the local and then, under a stronger assumption, the global classical solvability of the coagulation-fragmentation equation considered as a semilinear perturbation of the linear fragmentation equation. Furthermore, we show that weak solutions of the coagulation--fragmentation equation, obtained by the weak compactness method, coincide with the classical local in time solutions provided the latter exist.