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Extended gradient systems: Dimension one

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  • We propose a general theorey of formally gradient differential equations on unbounded one-dimensional domains, based on an energy-flow inequality, and on the study of the induced semiflow on the space of probability measures on the phase space. We prove that the $\omega$-limit set of each point contains an equilibrium, and that the $\omega$-limit set of $\mu$-almost every point in the phase space consists of equilibria, where $\mu$ is any Borel probability measure invariant for spatial translation.
    Mathematics Subject Classification: 37B35, 35B40.


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