On a moving boundary problem associated with the swelling drug release platforms

ABSTRACT

This paper studies a parabolic-type system of time-dependent partial differential equations coupled with Robin boundary conditions to model the solvent penetration and subsequently a controlled drug release from a swellable polymeric spherical platform. The model's key feature is that the solvent penetration and the polymer swelling result in moving boundaries. From an analytical perspective, some properties of the solutions, such as the positivity and the uniqueness of the solutions, are established. A second-order iterative procedure based on the backward finite difference method is carried out to solve the problem numerically. Finally, the numerical results and the asymptotic solutions are compared, intending to illustrate the validity and applicability of the numerical scheme.

KEYWORDS:

• Moving boundary problem
• swelling polymeric platform
• maximum principle
• uniqueness
• drug release
• iterative procedure

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35k20
• 65M06
• 92-08

Disclosure statement

No potential conflict of interest was reported by the author(s).