On the asymptotic behaviour of the characteristics in the codiffusion of radioactive isotopes with general initial data

The large-time behaviour of the solution of a hyperbolic- parabolic problem in an isolated domain, which models the diffusion of n species of radiative isotopes of the same element, is studied, assuming general hypotheses on the initial data. Depending on the radiative law and on the distribution of the initial concentration, either a uniform distribution for the concentration of each isotope or the presence of oscillations may be possible when t → ∞

On a multidimensional model for the codiffusion of isotopes: localization and asymptotic behavior

The paper deals with a system of parabolic\u2013hyperbolic partial differential equations, which models the diffusion of N species of isotopes of the same element, possibly radioactive, in a multidimensional medium. Some qualitative properties of the solutions, such as localization property, are studied together with the asymptotic behavior for large times

On a Quasilinear Parabolic System Modelling the Diffusion of Radioactive Isotopes

We consider a model for the diffusion of N species of isotopes of the same element in a medium, consisting in a parabolic quasilinear system, with Dirichlet boundary condition, in the general hypothesis that the diffusion coefficients possibly are all different. We prove existence and uniqueness of classical solution in the physically relevant assumption that the total concentration of the element is positive and bounded

Numerical Results for the Codiffusion of Isotopes

Numerical simulations have been performed for a model for the distribution of radionuclides in the ground water around a deep repository for used nuclear fuel, based on the assumption that different isotopes of the same chemical element A contribute jointly to the chemical potential of A, through two different components of the flux. The corresponding problem consists in a parabolic system strongly coupled, that, in the physically relevant assumption that one of these components is negligible, reduces to a parabolic equation for the total concentration of the element A, possibly coupled with hyperbolic equations for the concentrations of the single isotopes. These simulations evidentiate the qualitative behaviour of the solution in dependence of the diffusion oefficients, showing striking effects that can be observed when one of the component of the flux is much smaller than the other. [DOI: 10.1685/CSC09231] About DOIViene studiato mediante simulazioni numeriche un modello per la distribuzione di isotopi radioattivi dispersi nel terreno circostante depositi di scorie nucleari, basato sull’ipotesi che il potenziale chimico dell’elemento stesso sia costituito da due componenti, una dovuta alle interazioni tra differenti isotopi Ai dello stesso elemento A, e l’altra alle interazioni degli isotopi con le molecole del solvente B. Il problema è un sistema parabolico fortemente accoppiato, che, nell’ipotesi che la seconda di queste componenti sia trascurabile, si riduce a un’equazione parabolica per la concentrazione totale dell'elemento A, accoppiata con equazioni iperboliche per la concentrazione dei singoli isotopi. Le simulazioni numeriche evidenziano la dipendenza delle soluzioni dai coefficienti di diffusione, sia per isotopi stabili che per isotopi radioattivi, e ci permettono di analizzare gli effetti di "frazionamento" riscontrabili nelle osservazioni. [DOI: 10.1685/CSC09231] About DO

A melting problem with a mushy region: qualitative properties

We consider a model problem of heat conduction in a slab where melting is produced by distributed heat sources. The same problem was considered by Atthey (1974) who produced numerical evidence of the appearance of a region (called a mushy region) where die temperature is identically equal to the melting temperature. Atthey's results were based on a weak formulation. Following Primiccrio (1982) this problem can be given a classical formulation as a three-phase problem with specific conditions at the interfaces (free boundaries). Here, referring to this classical formulation, we investigate some relevant properties of the solution and we give a fairly accurate description of the boundary of the mushy region

The Cauchy Problem for Degenerate Parabolic Equations with Source and Damping

We prove optimal estimates for the decay of mass of solutions to the Cauchy problem for a wide class of quasilinear parabolic equations with damping terms. In the degenerate case, we also prove estimates for the finite speed of propagation. When the equation contains also a blow up term, we discuss existence and nonexistence of global solutions

Advances in Mathematical SHOCK PROPAGATION IN A FLOW THROUGH DEFORMABLE POROUS MEDIA: POSSIBLE DEGENERATION OF THE HYPERBOLIC PROBLEM

Abstract We consider a one-dimensional incompressible flow through a porous medium undergoing deformations, where the porosity depends on the flux intensity up to a threshold value, after which it remains constant. This assumption implies that the hyperbolic problem becomes degenerate. ---------------- Communicated by Editors; Receive