The Classical Stefan Problem: basic concepts, modelling and analysis (0444510869)

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This volume emphasises studies related to

classical Stefan problems. The term "Stefan problem" is

generally used for heat transfer problems with

phase-changes such

as from the liquid to the solid. Stefan problems have some

characteristics that are typical of them, but certain problems

arising in fields such as mathematical physics and engineering

also exhibit characteristics similar to them. The term

``classical" distinguishes the formulation of these problems from

their weak formulation, in which the solution need not possess

classical derivatives. Under suitable assumptions, a weak solution

could be as good as a classical solution. In hyperbolic Stefan

problems, the characteristic features of Stefan problems are

present but unlike in Stefan problems, discontinuous solutions are

allowed because of the hyperbolic nature of the heat equation. The

numerical solutions of inverse Stefan problems, and the analysis of

direct Stefan problems are so integrated that it is difficult to

discuss one without referring to the other. So no strict line of

demarcation can be identified between a classical Stefan problem

and other similar problems. On the other hand, including every

related problem in the domain of classical Stefan problem would

require several volumes for their description. A suitable

compromise has to be made.

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