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arXiv · 2509.01316

The continuous version of the generalized exchange-driven growth model

Prasanta K. Barik·Fernando P. da Costa·João T. Pinto·Rafael Sasportes
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Abstract

In this article, we discuss the continuous version of the generalized exchange-driven growth model which is a variant of the coagulation model in which a smaller size particle is detached from a bigger one and merges with another particle. This new model is a continuous extension of the generalized exchange-driven growth model originally formulated in a discrete context [4]. In this work, we examine the existence of weak solutions to the continuous version of the generalized exchange-driven growth model under a suitable reaction rate. Under an additional condition on the reaction rates, a uniqueness result is established. Finally, we prove that solutions satisfy the mass-conserving property and the conservation of the total number of particles for coagulation rates with linear bounds.

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Prasanta K. Barik, Fernando P. da Costa, João T. Pinto, Rafael Sasportes. 2025-09-01. The continuous version of the generalized exchange-driven growth model. https://arxiv.org/abs/2509.01316

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