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Mathematical models of some diffusive processes with free boundaries. (English) Zbl 1122.35001

MAT. Serie A: Conferencias, Seminarios y Trabajos de Matemática 11. Rosario: Universidad Austral, Departamento de Matemática. 128 p. (2005).
The notes under review are outgrowth of a series of lectures taught by the author at the Scuola Normale Superiore di Pisa to the students of the Ph.D. program “Mathematics for industrial technologies”. Their general purpose is to provide various examples of how a mathematical model for a given process can be formulated starting from some basic physical information. The author’s attention is concentrated on problems including linear diffusion and characterized by the presence of free boundaries, the main prototype of which is the celebrated Stefan problem.
The notes start with basic theoretical facts about the heat equation and Stefan-type problems (classical and weak solvability) which form the background for the remaining part devoted mainly to the modelling. Various problems of industrial relevance (either classical or very recent) are illustrated such as reaction-diffusion processes with dead cores, the oxygen diffusion-consumption, the Bingham flows, processes in porous media, deposition of solid wax from crude oils, diffusive processes in tumour cords and modelling of Ziegler-Natta polymerization.

MSC:

35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35R35 Free boundary problems for PDEs
80A22 Stefan problems, phase changes, etc.
82D60 Statistical mechanics of polymers
92C37 Cell biology
76S05 Flows in porous media; filtration; seepage
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