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In this paper, we investigate the use of so called "duality lemmas" to studythe system of discrete coagulation-fragmentation equations with diffusion. Whenthe fragmentation is strong enough with respect to the coagulation, we showthat we have creation and propagation of superlinear moments. In particularthis implies that strong enough fragmentation can prevent gelation even forsuperlinear coagulation, a statement which was only known up to now in thehomogeneous setting. We also use this control of superlinear moments to extenda recent result about the regularity of the solutions in the pure coagulationcase, to strong fragmentation models.

Applications of improved duality lemmas to the discrete coagulation-fragmentation equations with diffusion