Cordwell, William R: In solid rocket motors, it can be desirable to have a roughly constant burning (surface) area. One solution is to start out with a star shaped hole down the middle; the star erodes as it burns, but the hole also gets larger. Of course, the outside surface is not burning in this case, so it doesn't directly apply to the fertilizer question, but it seems as though you could have a cylinder with an inside hole that gets larger at a similar rate as the outside surface gets smaller.
--actually, the "obvious" 2D solution I had in mind was an annulus (ring between two concentric circles) which erodes from the inside and outside simultaneously to have constant surface. But this solution would not be good as a solid rocket since for that we want erosion from inside ONLY. But stimulated by Cordwell, I realize it actually is possible to have a 2D "rocket" solution in 2D which really only erodes from inside and really does have constant surface area for some positive timespan. Make the inward (concave) points of the star-shaped hole have angles A1,A2,...An and make the outward-pointing (convex) vertices have angles B1,B2,...,Bn. Then constant surface happens if and only if 2 * sum_k cot(Ak / 2) = sum_k (2*pi - Bk). Note that necessarily sum_k (Ak-Bk) = 2*pi. It similarly is possible to erode a star-shaped polygon from the outside only while enjoying constant surface for a positive timespan, but then the constancy CANNOT persist the whole way (until it is eroded away to nothing); that ONLY is possible with a topology (e.g. an annulus) more complicated than just a union of disjoint disks. Also, if we restrict ourselves to smooth surfaces (polygons due to corners are disqualified) then constancy for even a positive timespan, no matter how small, is impossible in 2D unless you have annulus topology.