Periodically growing solutions in a class of strongly monotone semiflows

Abstract

We study the behavior of unbounded global orbits in a class of stronglymonotone semiflows and give a criterion for the existence of orbitswith periodic growth. We also prove the uniqueness and asymptoticstability of such orbits. We apply our results to a certain class ofnonlinear parabolic equations including a weakly anisotropic curvatureflow in a two-dimensional annulus and show the convergence of the solutionsto a periodically growing solution which grows up in infinite timechanging its profile time-periodically.