Stability of ternary reaction-diffusion dynamical systems

Abstract

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.