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.
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