Difusión no Lineal: Resolución Numérica de una Ecuación de Reacción-Difusión

Abstract

With a nonlinear parabolic model, with Dirichlet boundary conditions, we make numeric experiences to approximate non trivial solutions, for t→ ∞ assyntotically stables, that is solutions that tend to the elliptic problem, in the Lyapunov sense [1,2,3].
The model belongs to the so-called reaction-diffusion equations of semilinear kind, that are linear in the heat operator and have a nonlinear reaction function, in this case
f (u,a,b) = u (a - b u), being u conce~llration, a and b parameters [4].
The used algorithm is based on the concept of monotone and ordered sequences [5], and on the existence theorem of Amann and Sattinger [1].