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In some cases mathematical models of physical or biological phenomena do not return the laws of nature used to build them. Well‐known examples of this type appear in fragmentation‐coagulation theory or in birth‐and‐death processes, as well as in some branches of transport theory. In these examples models based on the principle of conservation of mass (individuals, or particles) have solutions that are not conservative. In this paper we consider such models, augmented by diffusion in the physical space, and show that the diffusive part does not affect the breach of the conservation laws.
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