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.
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Transcribed Image Text: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<ti and for tį > t.
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Suppose that particles move only by diffusion. Suppose that a number of particles are injected at r = 0 at time t = 0, and other particles are injected at r = 0 at time > 0. Write down the function N(x, t) that gives the number density of particles at location r at time t, as following below.
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