La diffusione del calore in uno strato di spessore variabile in presenza di scambi termici non lineari con l'ambiente. (I) Deduzione di limitazioni a priori sulla temperatura e le sue derivate
Wax deposition in crude oils: a new approach
The complex phenomenon of solid wax deposition in wax saturated crude oils subject to thermal gradients has been treated in a number of papers under very specific assumptions (e.g. thermodynamical equilibrium between dissolved wax and the wax suspended in the oil as a crystallized phase). Here we want to consider a more general framework in which thermodynamical equilibrium may not exist, the whole system may form a gel-like structure in which the segregated solid wax has no diffusivity, the thermal...
One phase and two-phase free boundary problems of general type for the heat equation
Vengono enunciati teoremi di esistenza ed unicità per le soluzioni di problemi a contorno libero per l'equazione unidimensionale del calore. I risultati riguardano ampie classi di problemi a una e a due fasi.
Oxygen exchange between multiple capillaries and living tissues: An homogenisation study
A mathematical model for a problem of blood perfusion in a living tissue through a system of parallel capillaries is studied. Oxygen is assumed to be transported in two forms: freely diffusing and bounded (to erytrocytes in blood, to myoglobin in tissue). Existence of a weak solution is proved and a homogensation procedure is carried out in the case of randomly distribuited capillaries.
Asymptotic behaviour of the interface for the critical case of undercooled Stefan problem
The critical case of solvability of a two-phase Stefan problem with supercooled liquid phase is considered. Asymptotic analysis is performed of the behaviour of the free boundary in the vicinity of the initial time.
Modelling bioremediation of polluted soils in unsaturated condition and its effect on the soil hydraulic properties
We study the unsaturated flow of an incompressible liquid carrying a bacterial population through a porous medium contaminated with some pollutant. The biomass grows feeding on the pollutant and affecting at the same time all the physics of the flow. We formulate a mathematical model in a one-dimensional setting and we prove an existence theorem for it. The so-called fluid media scaling approach, often used in the literature, is discussed and its limitations are pointed out on the basis of a specific...
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