An exact analytical solution to the non-stationary coagulation equation
describing the endosomal network dynamics
Motivated by important applications in materials science and biology, we
consider a non-stationary coagulation equation with in-flux and out-flux
of particles (cargo). An exact analytical solution to this
integrodifferential equation is found in a parametric form. This
solution behaves as a decaying exponent with respect to the particle
volume (fluorescence intensity in the case of coagulation of endosomes).
We demonstrate that our exact solution substantially depends on
coagulation kernels (fusion and fission rates) as well as the in-flux
and out-flux processes of cargo.