The spreading of a toxic waste that decays in time is often modeled by the diffusion equation dC 82C „ £( , k + C f{t) where a denotes the decay rate and /(x, t) the source strength per unit distance and unit time. Let the domain be 0 < x < L and no flux be permitted at both ends. Initially the concentration is zero everywhere. Find C(x, t) for t > 0 for general /. Discuss the result for the following special source function /: f/is(^) forT, where fo is a constant. Comment on the effect of the decay rate.