Let c(x, y, z, t) denote the concentration of a pollutant (the amount per unit volume).
(a) What is an expression for the total amount of pollutant in the region R?
(b) Suppose that the flow J of the pollutant is proportional to the gradient of the concentration. (Is this reasonable?) Express conservation of the pollutant.
(c) Derive the partial differential equation governing the diffusion of the pollutant.
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