Existence, uniqueness, stability and asymptotic behavior of solutions for a mathematical model of atherosclerosis

Telma  Silva; Adélia Sequeira; Rafael F. Santos; Jorge  Tiago

doi:10.3934/dcdss.2016.9.343

Article Contents

2016, Volume 9, Issue 1: 343-362. Doi: 10.3934/dcdss.2016.9.343

This issue Previous Article Local well-posedness of free surface problems for the Navier-Stokes equations in a general domain Next Article

Existence, uniqueness, stability and asymptotic behavior of solutions for a mathematical model of atherosclerosis

1.
Uni-CV, Cabo Verde and CEMAT, IST, Universidade de Lisboa, 1049-001 Lisbon
2.
Department of Mathematics and CEMAT/IST, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa
3.
Department of Mathematics and CEMAT/IST, Faculty of Sciences and Technology, University of Algarve, Campus de Gambelas 8005-139 Faro
4.
Dept Math and CEMAT, IST, Universidade de Lisboa, 1049-001 Lisbon

Received: September 2014

Revised: February 2015

Published: February 2016

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Abstract

We study an atherosclerosis model described by a reaction-diffusion system of three equations, in one dimension, with homogeneous Neumann boundary conditions. The method of upper and lower solutions and its associated monotone iteration (the monotone iterative method) are used to establish existence, uniqueness and boundedness of global solutions for the problem. Upper and lower solutions are derived for the corresponding steady-state problem. Moreover, solutions of Cauchy problems defined for time-dependent system are presented as alternatives upper and lower solutions. The stability of constant steady-state solutions and the asymptotic behavior of the time-dependent solutions are studied.

Keywords:

Mathematics Subject Classification: Primary: 35K57, 92C50; Secondary: 35A01, 35A08, 35B35, 35B40.

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