Doctor of Philosophy
Department of Mathematics
Kucera, Adam, Mathematics of moving boundary problems in diffusion, Doctor of Philosophy thesis, Department of Mathematics, University of Wollongong, 1985. https://ro.uow.edu.au/theses/1553
This thesis is concerned with the development, generahzation and apphcation of a formal series technique for classical one-dimensional moving boundary diffusion problems. The solution procedure consists of two major steps. Firstly, the introduction of a boundary fixing transformation, which fixes the moving boundary and simplifies the transformed equations. Secondly, the assumption of a formal series solution which leads to a system of ordinary differential equations for the unknown coefficients in the series. The method generalizes to multi-phase and heterogeneous moving boundary problems for both constant temperature and Newton's radiation conditions and yields simple and highly accurate estimates for both the temperature and boundary motion.