Differential and Integral Equations

Structurally damped plate and wave equations with random point force in arbitrary space dimensions

Roland Schnaubelt and Mark Veraar

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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.

Article information

Differential Integral Equations, Volume 23, Number 9/10 (2010), 957-988.

First available in Project Euclid: 20 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]


Schnaubelt, Roland; Veraar, Mark. Structurally damped plate and wave equations with random point force in arbitrary space dimensions. Differential Integral Equations 23 (2010), no. 9/10, 957--988. https://projecteuclid.org/euclid.die/1356019119

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