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Drug release enhanced by temperature: an accurate discrete model for solutions in \(H^3\). (English) Zbl 07256630
Summary: In this paper we consider the coupling between two quasilinear diffusion equations: the diffusion coefficient of the first equation depends on its solution and the diffusion and convective coefficients of the second equation depend on the solution of the first one. This system can be used to describe the drug evolution in a target tissue when the drug transport is enhanced by heat. We study, from an analytical and a numerical viewpoints, the coupling of the heat equation with the drug diffusion equation. A fully discrete piecewise linear finite method is proposed to solve this system and its stability is studied. Assuming that the heat and the concentration are in \(H^3\) we prove that the method is second order convergent. Numerical experiments illustrating the theoretical results and the global qualitative behaviour of the coupling are also included.

MSC:
92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
35K57 Reaction-diffusion equations
65N06 Finite difference methods for boundary value problems involving PDEs
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