The Stefan problem is a class of problems in mathematical physics that involve determining the temperature distribution in a medium undergoing a phase change, such as ice melting to water. It is characterized by a moving phase boundary whose position is determined as part of the solution, guided by Stefan's condition which connects the latent heat at the boundary to the heat flux in the material.
A Moving Boundary Problem involves the study of physical phenomena where the boundary of the domain changes with time, necessitating a dynamic and adaptive approach to modeling and analysis. These problems are prevalent in fields such as fluid dynamics, heat transfer, and material science, where they describe processes like phase changes, diffusion, and growth phenomena.
Degenerate diffusion refers to a class of diffusion processes where the diffusivity becomes zero or vanishes in certain regions, leading to a qualitative change in the behavior of the solution. These phenomena often appear in mathematical models of physical processes such as filtration, phase transitions, and biological growth, where standard diffusion equations do not adequately capture the complexity of the system dynamics.