Abstract
We consider the singularly perturbed parabolic differential equation under the assumption that f is T-periodic in t and that the degenerate equation f(u, x, t, 0) = 0 has two intersecting roots. In a previous paper [V.F. Butuzov, N.N. Nefedov, L. Recke, and K.R. Schneider, On a class of periodic solutions of a singularly perturbed parabolic problem, J. Math. Anal. Appl. 348 (2008), pp. 508--515] we presented conditions under which there exists an asymptotically stable T-periodic solution u p (x, t, ϵ) satisfying no-flux boundary conditions. In this note we characterize a set of initial functions belonging to the region of attraction of u p (x, t, ϵ).
Acknowledgements
This work was partially supported by RFBR-DFG grant, the program of cooperation of the Moscow State University and the Humboldt University of Berlin, and RFBR grant N08-01-00413.