2. Suppose that particles move only by diffusion. Suppose that a number No of particles are injected at z = 0 at time t = 0, and another N1 particles are injected at r = 0 at time ti > 0. Write down the function N(r,t) that gives the number density of particles at location r at time t. Hint: The PDE is linear so you can add solutions. Note that you will have different formulas for 0 t.

2. Suppose that particles move only by diffusion. Suppose that a number No of particles are injected at z = 0 at time t = 0, and another N1 particles are injected at r = 0 at time ti > 0. Write down the function N(r,t) that gives the number density of particles at location r at time t. Hint: The PDE is linear so you can add solutions. Note that you will have different formulas for 0 t.