Conference publications

An averaging method for singularly perturbed systems of semilinear differential inclusions with hysteresis nonlinearities

Gudovich A.N.


"Математика. Компьютер. Образование". Cб. трудов X международной конференции. Под общей редакцией Г.Ю. Ризниченко Ижевск: Научно-издательский центр "Регулярная и хаотическая динамика", 2003. Vol. 2. Pp. 137-141.

We consider a singularly perturbed system of semilinear parabolic inclusions containing high frequency terms and hysteresis nonlinearity. For such systems we justify the averaging principle, which is an analog of classical averaging theorem of N. N. Bogolyubov – N. M. Krilov. Our assumptions permit to define an upper semicontinuous, compact vector operator whose fixed points determine periodic solutions of original system. The existence of fixed point of constructed multivalued operator is shown by using topological degree theory.

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