| Contents |
| We study an diffusion -- reaction mathematical model
for the evolution of atherosclerosis as an inflammation disease.
A high order finite volume formulation in the context of ADER approach is
developed to approximate the time-dependent solutions of the model
proposed by El Khatib et al. (2007).
Concerning the asymptotic behaviour of the solutions, the numerical
examples show that a small perturbation of a healthy steady state
makes the system evolve to a disease equilibrium for some choice of
the parameters. We apply our numerical scheme to determine
if each initial datum in a huge
family of initial data is attracted by a disease equilibrium or by
a healthy steady state. Simultaneously we compute the steady states. This is a joint work with L. Tello (Universidad Polit\'ecnica de Madrid) and E.F. Toro (Universit\`a degli Studi di Trento). |
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