Analysis and numerical solution of nonlinear Volterra partial integrodifferential equations modeling swelling porous materials

A nonlinear Volterra partial integrodifferential equation (VPIDE), derived using hybrid mixture theory and used to model swelling porous materials, is analyzed and solved numerically. The model application is an immersed porous material imbibing fluid through a cylinder’s exterior boundary. A poignant example comes from the pharmaceutical industry where controlled release, drugdelivery systems are comprised of materials that permit nearly constant drug concentration profiles. In the considered application the release is controlled by the viscoelastic properties of a porous polymer network that swells when immersed in stomach fluid, consequently increasing the pore sizes and allowing the drug to escape. The VPIDE can be viewed as a combination of a non-linear diffusion equation and a constitutive equation modeling the viscoelastic effects. The viscoelastic model is expressed as an integral equation, thus adding an integral term to the non-linear partial differential equation. While this integral term poses both theoretical and numerical challenges, it provides fertile ground for interpretation and analysis. Analysis of the VPIDE includes an existence and uniqueness proof which