Suppose we have a long tube, modeled as the interval (OL) filled with water. We inject droplets of ink in the middle of the tube at certain discrete time events ti = iT , i = 1.2….. Argue why the...

Suppose we have a long tube, modeled as the interval (OL) filled with water. We inject droplets of ink in the middle of the tube at certain discrete time events ti = iT , i = 1.2….. Argue why the following source function is a reasonable model for such a type of injection:

Here, K is a constant reflecting the mount of mass injected. Hint: Make sketches of (o, better yet, animate) the function f(xt) . Set up a one-dimensional PDE model with appropriate boundary and initial conditions for this problem. How do you expect the solution to develop in time?