On the stability of equilibria to weakly coupled parabolic systems in unbounded domains Original Research Article

We investigate weakly coupled semilinear parabolic systems in unbounded domains of R2R2 or R3R3 with general nonlinearities. We present several sufficient conditions on the nonlinearities which ensure the stability of the zero solution with respect to H2H2-perturbations. In addition, various examples are discussed to illustrate the scope of application of our results.