Symmetry and convergence properties for non-negative solutions of nonautonomous reaction–diffusion problems
Peter Heß, Peter Poláčik · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1994
Nonautonomous parabolic equations of the form ut − Δu = f(u, t) on a symmetric domain are considered. Using the moving-hyperplane method, it is proved that any bounded nonnegative solution symmetrises as t → ∞. This is then used to show that for nonlinearities periodic in t, any non-negative bounded solution approaches a periodic solution.