The finite speed of propagation for solutions to nonlinear stochastic wave equations driven by multiplicative noise

Barbu V, Röckner M (2013)
Journal Of Differential Equations 255(3): 560-571.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Barbu, Viorel; Röckner, MichaelUniBi
Abstract / Bemerkung
We prove that the solutions to the stochastic wave equation in O subset of R-d, d(X) over dot - Delta X dt + g(X) dt = sigma(X)dW, for 1 <= d <= infinity, where g is a continuous function with polynomial growth of order less or equal to d/ d-2 and sigma is Lipschitz with sigma(0) = 0, propagate with finite speed. This result resembles the classical finite speed of propagation result for the solution to the Klein-Gordon equation and extends to equations with dissipative damping. A similar result follows for the equation with additive noise of the form F(t)dW, where F(t) = F(t, xi) has compact support (in xi) for each t > 0. (C) 2013 Elsevier Inc. All rights reserved.
Stichworte
Wave equation; Stochastic equation; Sobolev spaces; Wiener process
Erscheinungsjahr
2013
Zeitschriftentitel
Journal Of Differential Equations
Band
255
Ausgabe
3
Seite(n)
560-571
ISSN
0022-0396
Page URI
https://pub.uni-bielefeld.de/record/2607125

Zitieren

Barbu V, Röckner M. The finite speed of propagation for solutions to nonlinear stochastic wave equations driven by multiplicative noise. Journal Of Differential Equations. 2013;255(3):560-571.
Barbu, V., & Röckner, M. (2013). The finite speed of propagation for solutions to nonlinear stochastic wave equations driven by multiplicative noise. Journal Of Differential Equations, 255(3), 560-571. doi:10.1016/j.jde.2013.04.022
Barbu, V., and Röckner, M. (2013). The finite speed of propagation for solutions to nonlinear stochastic wave equations driven by multiplicative noise. Journal Of Differential Equations 255, 560-571.
Barbu, V., & Röckner, M., 2013. The finite speed of propagation for solutions to nonlinear stochastic wave equations driven by multiplicative noise. Journal Of Differential Equations, 255(3), p 560-571.
V. Barbu and M. Röckner, “The finite speed of propagation for solutions to nonlinear stochastic wave equations driven by multiplicative noise”, Journal Of Differential Equations, vol. 255, 2013, pp. 560-571.
Barbu, V., Röckner, M.: The finite speed of propagation for solutions to nonlinear stochastic wave equations driven by multiplicative noise. Journal Of Differential Equations. 255, 560-571 (2013).
Barbu, Viorel, and Röckner, Michael. “The finite speed of propagation for solutions to nonlinear stochastic wave equations driven by multiplicative noise”. Journal Of Differential Equations 255.3 (2013): 560-571.

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