Periodically growing solutions in a class of strongly monotone semiflows | Zendy

Ken-Ichi Nakamura | Zendy; Toshiko Ogiwara | Zendy

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Periodically growing solutions in a class of strongly monotone semiflows

Author(s) -

Ken-Ichi Nakamura,

Toshiko Ogiwara

Publication year - 2012

Publication title -

networks and heterogeneous media

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.732

H-Index - 34

eISSN - 1556-181X

pISSN - 1556-1801

DOI - 10.3934/nhm.2012.7.881

Subject(s) - uniqueness , monotone polygon , mathematics , class (philosophy) , annulus (botany) , convergence (economics) , mathematical analysis , pure mathematics , computer science , geometry , biology , botany , artificial intelligence , economics , economic growth

We study the behavior of unbounded global orbits in a class of strongly monotone semiflows and give a criterion for the existence of orbits with periodic growth. We also prove the uniqueness and asymptotic stability of such orbits. We apply our results to a certain class of nonlinear parabolic equations including a weakly anisotropic curvature flow in a two-dimensional annulus and show the convergence of the solutions to a periodically growing solution which grows up in infinite time changing its profile time-periodically.

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