In this paper a non linear mathematical model to describe absorption phenomena in polymers\ud is proposed. The model is established assuming that the diffusing penetrant causes a\ud deformation which induces a viscoelastic stress responsible for a convective field. This convective\ud field is defined to represent an opposition of the polymer to the Fickian diffusion.\ud Several numerical examples show the effectiveness of the model

A three-dimensional mathematical model for sorption/desorption by a cylindrical polymeric matrix with dispersed drug is proposed. The model is based on a system of partial differential equations coupled with boundary conditions over a moving boundary. We assume that the penetrant diffuses into a swelling matrix and causes a deformation, which induces a stressdriven diffusion and consequently a non-Fickian mass flux. A physically sound nonlinear dependence between strain and penetrant concentration is considered and introduced in a Boltzmann integral with a kernel computed from a Maxwell-Wiechert model. Numerical simulations show how the mechanistic behavior can have a role in drug delivery design. Introduction.In this paper we study a three-dimensional model of diffusion of a solvent into a cylindrical polymeric matrix containing drug and followed by the drug release. To describe drug release from a polymeric matrix, several models have been proposed [11,12,13,15,18,25,27]. However to the best of our knowledge, the influence of the mechanical properties of a swelling polymer in the sorption of a solvent and in the desorption of drug has not yet been considered in the literature. We propose a model where we combine non-Fickian sorption of the liquid agent, non-Fickian desorption, coupled with nonlinear dissolution and polymer swelling.It is well known that the diffusion of a liquid agent into a polymeric sample cannot be completely described by Fick's classical law. The liquid strains the polymeric matrix that, while swelling, exerts a stress that acts as a barrier to the incoming fluid. To explain these phenomena several authors [2,4,5,11,22,23,24] agree that a modified flux must be considered, that is

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A mathematical model which simulates drug delivery through the cornea, from a therapeutic lens to the anterior chamber of the eye, is proposed. The model consists of three coupled systems of partial differential equations linked by interface conditions: drug diffusion in the therapeutic lens; diffusion and metabolic consumption in the cornea; diffusion, convection and metabolic consumption in the anterior chamber of the eye. The dependence of intraocular pressure on the obstruction of the trabecular mesh and the production rate of aqueous humor by the ciliary body is modeled. The therapeutic effects of drugs that act on the trabecular mesh or on the ciliary body are analysed. Comparisons between topical administration and drug delivery from a therapeutic lens are included.

In this article the qualitative properties of numerical traveling wave solutions for integrodifferential equations, which generalize the well known Fisher equation are studied. The integro-differential equation is replaced by an equivalent hyperbolic equation which allows us to characterize the numerical velocity of traveling wave solutions. Numerical results are presented.