Kinetics of differentiation/continuous model.
a. Derive the first-order PDE that describes the population balance.
b. Make time dimensionless relative to the rate of differentiation.
c. Describe the two resulting dimensionless groups (call the dimensionless group for apoptosis A, and the one for the cell cycle B).
d. Solve the equation in steady state for A = 0.
e. Solve the equation(s) where A is nonzero for a portion of the differentiation process (i.e., between a1 and a2). f. Solve the transient equation for A = 0.