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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Abstract

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

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

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019119

Mathematical Reviews number (MathSciNet)
MR2675589

Zentralblatt MATH identifier
1240.60189

Subjects
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]

Citation

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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