  We consider a class of convex optimization problems modelling temporal mass
transport and mass change between two given mass distributions (the so-called
dynamic formulation of unbalanced transport), where we focus on those models
for which transport costs are proportional to transport distance. For those
models we derive an equivalent, computationally more efficient static
formulation, we perform a detailed analysis of the model optimizers and the
associated optimal mass change and transport, and we examine which static
models are generated by a corresponding equivalent dynamic one. Alongside we
discuss thoroughly how the employed model formulations relate to other
formulations found in the literature.
