# American Institute of Mathematical Sciences

February  2016, 9(1): 343-362. doi: 10.3934/dcdss.2016.9.343

## 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, Portugal 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, Portugal 4 Dept Math and CEMAT, IST, Universidade de Lisboa, 1049-001 Lisbon, Portugal

Received  September 2014 Revised  February 2015 Published  December 2015

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.
Citation: Telma Silva, Adélia Sequeira, Rafael F. Santos, Jorge Tiago. Existence, uniqueness, stability and asymptotic behavior of solutions for a mathematical model of atherosclerosis. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 343-362. doi: 10.3934/dcdss.2016.9.343
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