On monotonicity of solutions to mixed problems for weakly coupled cooperative parabolic systems (Q1920690)

The authors deal with stabilization (convergence to an equilibrium) and quasistabilization (convergence to a set of equilibria) of solutions of quasilinear parabolic equations. They mostly (but not exclusively) focus their attention to one-dimensional second order equations. The paper surveys some known stabilization results and improves them in some aspects (e.g., extension to equations with degeneracies). Applicability of both continuous and discrete-valued Lyapunov functionals in the proof of stabilization is discussed.