Long-time behavior of solutions of a multi-dimensional electrophoretic model with a single reaction

In this dissertation, an electrophoretic model consisting of three charged species is considered. A dissociation-association reaction is allowed to take place between these species. The ions diffuse owing to concentration gradients and migrate because of electric force.

We prove that the steady state solution to the equations that govern this model exists and is unique. Moreover, we show that any initial distribution of species concentrations will settle down to this unique steady state as time becomes large. We also develop an algorithm for finding the numerical approximation to the unsteady state solutions of the governing equations.