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Structurally damped plate and wave equations with random point force in arbitrary space dimensions. (English) Zbl 1240.60189

Summary: In this paper we consider structurally damped plate and wave equations with point and distributed random forces. In order to treat space dimensions more than one, we work in the setting of \(L^{q}\)-spaces with (possibly small) \(q\in (1,2)\). We establish existence, uniqueness and regularity of mild and weak solutions to the stochastic equations employing recent theory for stochastic evolution equations in UMD Banach spaces.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
47N20 Applications of operator theory to differential and integral equations
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