A rigorous reduction of the L-2-stability of the solutions to a nonlinear binary reaction-diffusion system of PDE's to the stability of the solutions to a linear binary system of ODE's

摘要

A basic peculiar Lyapunov functional V is introduced for the dynamical systems generated by a pair of nonlinear reaction-diffusion PDE's, with nonconstant coefficients. The sign of V and of its derivative along the solutions is linked-through an immediate simple relation-to the eigenvalues. By using V and the L-2-norm, the non-linear L-2-stability (instability) is rigorously reduced to the stability (instability) of the solutions to a linear binary system of ODE's. (c) 2005 Elsevier Inc. All rights reserved.