The spatio-temporal oscillations of the Min-system are responsible for the prevention of mini-cells in E. coli by preventing FtsZ polymerization at the cell poles. These oscillations are studied in the context of cell growth and division. Models of cell growth via elongation and division are developed, and explored in conjunction with a biophysical reaction-diffusion model of the oscillations. Reaction-diffusion equations are solved numerically with model-specific dynamic boundary conditions using a Crank- Nicholson diffusion algorithm with linearized reaction terms. The model for elongation correctly captures the behavior of wild-type cells and predicts the emergence of multi-node oscillations in filamentous mutants. The model for cell division predicts that protein binding to the septum during division is important for preventing asymmetric oscillations in daughter cells. Future directions for theoretical work on this system will be discussed.