Bifurcation of self-oscillations of nonlinear parabolic equations with small diffusion

First, the questions of existence, multiplicity, and stability of timeperiodic solutions of the van der Pol equations with small diffusion are considered. It is shown that in some situations, the principle of averaging for parabolic equations plays a significant role in justifying these results. In this connection, the justification of the principle is given. At the end of the paper, it is indicated that the results allow one to investigate the well-known problem of the existence of spatially nonhomogeneous regimes in homogeneous media.
Bibliography: 26 titles.