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The discrete generalized exchange-driven system
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We study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and the coagulation-fragmentation system with binary fragmentation. Under reasonable general condition on the rate coefficients we establish the existence of admissible solutions, meaning solutions that are obtained as appropriate limit of solutions to a finite-dimensional truncation of the infinite-dimensional ODE. For these solutions we prove that, in the class of models we call isolated both the total number of particles and the total mass are conserved, whereas in those models we can non-isolated only the mass is conserved. Additionally, under more restrictive growth conditions for the rate equations we obtain uniqueness of solutions to the initial value problems.
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Cited by 2 Pith papers
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Existence and Non-existence for Exchange-Driven Growth Model
For exchange-driven growth, this paper extends global and local existence results and proves finite-time gelation and instantaneous gelation for fast-growing interaction kernels.
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The continuous version of the generalized exchange-driven growth model
The continuous exchange-driven growth model is well-posed: weak solutions exist for sum and product kernels, are unique under a sublinear rate condition, and conserve mass and particle number.
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