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Communicated by J. Vigo-AguiarA mathematical model to simulate drug delivery from a viscoelastic erodible matrix is presented in this paper. The drug is initially distributed in the matrix that is in contact with water. The entrance of water in the material changes the molecular weight, and bulk erosion can be developed depending on how fast this entrance is and how fast degradation occurs. The viscoelastic properties of the matrix also change in the presence of water as the molecular weight changes. The model is represented by a system of quasi-linear partial differential equations that take into account different phenomena: the uptake of water, the decreasing of the molecular weight, the viscoelastic behavior, the dissolution of the solid drug, and the delivery of the dissolved drug. Numerical simulations illustrating the behavior of the model are included. Copyright © 2015 John Wiley & Sons, Ltd.Keywords: drug delivery; molecular weight; bulk erosion; viscoelastic behavior; numerical simulation Mathematical modelWe consider a biodegradable viscoelastic polymeric matrix, Â R 2 , with boundary @ and containing a limited amount of drug. The matrix enters in contact with water, and as the water diffuses into the matrix, a hydration process, which modifies the viscoelastic properties of the polymer, takes place. The molecular weight decreases, and the drug starts to dissolve.In [1], a system that describes the sorption of water by a loaded erodible matrix and the release of drug was proposed. However, the viscoelastic properties of the matrix were not considered. In this paper, we present a general model, which generalizes the model in [1], by considering the viscoelastic behavior of the polymer (see for instance [2][3][4][5][6][7]).We consider a system of PDEs that describe the whole process: the entrance of water into the polymer and its consumption in the hydrolysis process, the decreasing of the molecular weight, the evolution of the stress and strain, and the dissolution and the diffusion of the dissolved drug. The system reads 8In (1), C W , C S , and C A represent the concentration of water, solid drug, and dissolved drug in the polymeric matrix, respectively, M is the molecular weight of the polymer, and is the stress response to the strain exerted by the water molecules. The first diffusion-reaction equation of (1) describes the diffusion of water into the matrix and its consumption in the hydrolysis. In this equation, D W represents the diffusion tensor of water in the polymeric matrix. We consider an isotropic medium where the

In this paper, we study a system of partial differential equations defined in a moving domain. This system is defined by a heat equation and a diffusion equation for a concentration of non-Fickian type whose diffusion coefficient depends on the temperature, completed with suitable initial and boundary conditions. The non-Fickian mass flux is established considering the viscoelastic properties of the medium where the strain depends on the temperature and on the concentration. The initial boundary value problem (IBVP) analyzed can be used to describe the drying of viscoelastic materials where the internal structure offers a resistance to the movement of the moisture molecules and a consequent delay in the moisture removal. Due to heat transference into the materials and moisture removal, shrinkage of the medium occurs. The stability of the IBVP defined in a moving domain is analyzed and its qualitative behavior is numerically studied.