Nonlinear diffusion in arterial tissues: a free boundary problem

A free boundary problem on a finite interval is formulated and solved for a nonlinear diffusion–convection equation. The model is suitable to describe drug diffusion in arterial tissues after the drug is released by an arterial stent. The problem is reduced to a system of nonlinear integral equation...

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Bibliographic Details
Published inActa mechanica Vol. 229; no. 10; pp. 4215 - 4228
Main Authors Burini, Diletta, De Lillo, Silvana, Fioriti, Gioia
Format Journal Article
LanguageEnglish
Published Vienna Springer Vienna 01.10.2018
Springer
Springer Nature B.V
Subjects
Analysis
Care and treatment
Classical and Continuum Physics
Control
Coronary heart disease
Diffusion
Dynamical Systems
Engineering
Engineering Thermodynamics
Free boundaries
Heat and Mass Transfer
Integral equations
Mathematical models
Nonlinear equations
Original Paper
Solid Mechanics
Stents
Surgical implants
Theoretical and Applied Mechanics
Vibration
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Summary:A free boundary problem on a finite interval is formulated and solved for a nonlinear diffusion–convection equation. The model is suitable to describe drug diffusion in arterial tissues after the drug is released by an arterial stent. The problem is reduced to a system of nonlinear integral equations, admitting a unique solution for small time. The existence of an exact solution corresponding to a moving front is also shown, which is in agreement with numerical results existing in the literature.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-018-2220-5