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Uniqueness of solutions for the extended Fisher-Kolmogorov equation. (English) Zbl 0913.34052
Summary: The authors considers stationary solutions to the extended Fisher-Kolmogorov (EFK) equation, a fourth-order model equation for bistable systems. As long as the stable equilibrium points are real saddles, the paths in the (u,u ' )-plane of two bounded solutions do not cross. As a consequence it is shown that the bounded solutions to the EFK equation correspond exactly to those to the classical Fisher-Kolmogorov equation.
MSC:
34F05ODE with randomness
60H30Applications of stochastic analysis
34C05Location of integral curves, singular points, limit cycles (ODE)