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Existence and stability of periodic solutions for parabolic systems with time delays. (English) Zbl 1130.35075
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.
35K50Systems of parabolic equations, boundary value problems (MSC2000)
35B10Periodic solutions of PDE
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