On the flux of diffusing matter through boundaries
Alan McNabb · Proceedings of the American Mathematical Society · 1962
in R for t> 0; u = uo, w = wo in X, the closure of R, at t =0; u = C(x, y, z, t) on dR for t > 0. Such systems govern the diffusion of a substance U of concentration u(x, y, z, t) which diffuses through a medium in accord with Fick's first law and simultaneously interacts with an immobile phase W. If w(x, y, z, t) is the local concentration of W, the principle of conservation of matter requires that u and w satisfy the differential equation