this paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. a model problem with nonlinear kinetic law is considered. the main result is an existence theorem. the mathematical effects of the kinetic term are discussed

The one-phase reduction of the Stefan problem, where the phase change temperature is a variable, is analysed. It is shown that problems encountered in previous analyses may be traced back to an incorrectly formulated Stefan condition. Energy conserving reductions for Cartesian, cylindrically and spherically symmetric problems are presented and compared with solutions to the two-phase problem.

The mathematical model of the movement of the shoreline in a sedimentary ocean basin (A Shoreline Problem) is a Stefan problem with variable latent heat. Swenson et al. [1] utilized an analogy with one-phase melting problem and developed a mathematical model for movement of shoreline in a sedimentary basin in response to changes in sediment line flux, tectonic subsidence of Earth's crust and se...

The non-local in space two-phase Stefan problem (a prototype phase change problems) can be formulated via a singular nonlinear parabolic integro-differential equation which admits unique weak solution. This formulation makes to part of the General Filtration Problems; class includes Porous Medium Equation. In this work, we prove that solutions both and Media problems are continuous.