Transient diffusion from high-capacity solute beacons (Q2184957)

The author considers a 2D diffusion problem for ``solute beacons'': high-concentration areas within a low-concentration infinite domain. The quasi-steady approximation is not accurate far from the beacon, thus are must solve the non-steady diffusion problem. Under the symmetry assumption, the dimensionless problem is solved by the Laplace transfrom and asymptotic expansion. The problem is posed for the 2D Fick diffusion equation in polar coordinates with zero initial condition and decay at infinity. Concentration within the beacon of the unit size decreases according to the conservation law, but the size remains constant.