Full Text: PDF
Received September 4, 2016; Accepted December 5, 2016; Published January 2, 2017
Abstract. Consider a parabolic PDE with the van der Pol cubic nonlinearity. The existence, structure and dimension of the attractor by classical theory of infinite-dimensional dynamical systems are summarized. The existence and attraction of the positive equilibrium or the negative equilibrium when parameters enter some regimes are verified. The stability of the trivial equilibrium by energy inequality and classical theory of reaction-diffusion equations are proved. Furthermore, we also give an answer to the question whether an eigenfunction of the Laplacian is attracted or repelled by the trivial equilibrium.
How to Cite this Article:
Bo Sun, Xinxin Gao, Dynamics of the parabolic equation due to van der Pol nonlinear distributed energy flows, Journal of Nonlinear Functional Analysis, Vol. 2017 (2017), Article ID 12, pp. 1-19.