Integro-differential models for percutaneous drug absorption

Abstract

In this paper we propose new mathematical models for percutaneous absorption of a drug. The new models are established by introducing, in the classical Fick's law, a memory term being the advection–diffusion equations of the classical models replaced by integro-differential equations. The well-posedness of the models is studied with Dirichlet, Neumann and natural boundary conditions. Methods for the computation of numerical solutions are proposed. Stability and convergence of the introduced methods are studied. Finally, numerical simulations illustrating the behaviour of the model are included.

Keywords:

• Convergence
• Integro-differential model
• Numerical approximation
• Stability

Acknowledgements

This work was supported by the Centre for Mathematics at the University of Coimbra.