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Periodic solutions of parabolic systems with nonlinear boundary conditions. (English) Zbl 0932.35111
The existence and the stability of periodic solutions for a coupled system of nonlinear parabolic equations under nonlinear boundary conditions is investigated. The method of upper and lower solutions and its associated monotone iterations is used. This method implies the existence of maximal and minimal periodic solutions, which can be computed from a linear iteration process in the same way as for parabolic initial-boundary value problems. A sufficient condition for the stability of a periodic solution is also given. These results are applied to models arising in chemical kinetics, ecology, and population biology.
MSC:
35K50Systems of parabolic equations, boundary value problems (MSC2000)
35B10Periodic solutions of PDE
35K55Nonlinear parabolic equations