Analysis of Smoluchowski’s Coagulation Equation with Injection
Eugenya V. Makoveeva,
Dmitri V. Alexandrov,
Sergei P. Fedotov
Affiliations
Eugenya V. Makoveeva
Laboratory of Stochastic Transport of Nanoparticles in Living Systems, Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000 Ekaterinburg, Russia
Dmitri V. Alexandrov
Laboratory of Stochastic Transport of Nanoparticles in Living Systems, Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000 Ekaterinburg, Russia
Sergei P. Fedotov
Department of Mathematics, The University of Manchester, Manchester M13 9PL, UK
The stationary solution of Smoluchowski’s coagulation equation with injection is found analytically with different exponentially decaying source terms. The latter involve a factor in the form of a power law function that plays a decisive role in forming the steady-state particle distribution shape. An unsteady analytical solution to the coagulation equation is obtained for the exponentially decaying initial distribution without injection. An approximate unsteady solution is constructed by stitching the initial and final (steady-state) distributions. The obtained solutions are in good agreement with experimental data for the distributions of endocytosed low-density lipoproteins.
