In view of the fundamental role played by the ternary reaction-di¤usion dynamical systems of P.D.Es for the description of the behaviour of continuous media and other phenomena (biological, chemical, …), this paper is devoted to their nonlinear _L_2-stability. General conditions guaranteeing the (local) nonlinear _L_2-stability via the stability of reduced or symmetric ternary linear systems of O.D.Es are found. The results obtained are applied to a triply convective-diffusive fluid mixture saturating a porous layer and to a biological problem.
Cite this article
Salvatore Rionero, Stability of ternary reaction-diffusion dynamical systems. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 22 (2011), no. 3, pp. 245–268DOI 10.4171/RLM/599