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Stability of stochastic partial differential equation

By Ruth F Curtain

Abstract

AbstractStochastic 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

Publisher: Published by Elsevier Inc.
Year: 1981
DOI identifier: 10.1016/0022-247X(81)90031-7
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