Stability of stochastic partial differential equation

Ruth F. Curtain*

*Corresponding author for this work

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    Abstract

    Stochastic partial differential equations such as occur in vibration problems for mechanical structures subjected to random loading are modelled as infinite dimensional stochastic Itô differential equations using a semigroup approach. Sufficient conditions for exponential stability of the expected energy of the system, as well as for the exponential decay of the sample paths of the displacement and velocity, are given. Under these same conditions it is shown that the zero solution is pathwise asymptotically stable relative to finite dimensional initial conditions. Illustrative examples are included.
    Original languageEnglish
    Pages (from-to)352-369
    Number of pages18
    JournalJournal of Mathematical Analysis and Applications
    Volume79
    Issue number2
    DOIs
    Publication statusPublished - 1981

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