A linear problem in diffusion in a region with a mobile boundary

The speed V(t) of the boundary is an arbitrary, continuous, and bounded function of time t. A mathematical model is derived, and a general method of solution based on thermal potentials is given. The particular case of V constant is considered. The solution is obtained as a sum of thermal potentials with unknown densities, which is reduced to a system of integral equations, which are solved by operational methods. The expression for the density of the potentials is obtained in a form suitable for further use.I am indebted to Professor G. M. Bartenev for direction and to Professor V. I. Levin and Dr. I. V. Razumovskaya for discussions of the results.