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Nonlinear diffusion in arterial tissues: a free boundary problem

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Perugia, Perugia, Italy

    Diletta Burini & Silvana De Lillo

  2. Department of Mathematics and Computer Science “Ulisse Dini”, University of Florence, Florence, Italy

    Gioia Fioriti

Authors
  1. Diletta Burini
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  2. Silvana De Lillo
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  3. Gioia Fioriti
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Correspondence to Diletta Burini.

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Burini, D., De Lillo, S. & Fioriti, G. Nonlinear diffusion in arterial tissues: a free boundary problem. Acta Mech 229, 4215–4228 (2018). https://doi.org/10.1007/s00707-018-2220-5

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  • DOI: https://doi.org/10.1007/s00707-018-2220-5

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