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Zbl 1130.35075
Wang, Changyou
Existence and stability of periodic solutions for parabolic systems with time delays. (English)
[J] J. Math. Anal. Appl. 339, No. 2, 1354-1361 (2008). ISSN 0022-247X

Summary: This paper is concerned with the existence and stability of time-periodic solutions for a class of coupled parabolic equations with time delay. Time delays may appear in the nonlinear reaction functions. The existence of time-periodic solutions is proved for a class of locally Lipschitz continuous reaction functions without any quasimonotone requirement. An approach to solve the problem is based on the method of upper and lower solution and Schauder fixed point theorem. Some other methods for proving the stability of the periodic solution are also given. The results for the general system can be applied to standard parabolic equations without time delay and corresponding ordinary differential systems. Finally, a model arising from chemistry is used to illustrate the obtained results.

MSC 2000:: *35K50 Systems of parabolic equations, boundary value problems
35B10 Periodic solutions of PDE

Keywords: periodic solution; upper and lower solution; stability; time delays; chemistry model

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