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The Cauchy problem for a nonlinear stochastic wave equation in any dimension

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Abstract.

A nonlinear wave equation on \( \mathbb{R}^d \) driven by a spatially homogeneous Wiener process is studied. Conditions for the existence of a function-valued solution in terms of the covariance kernel of the noise are given for an arbitrary dimension d.

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  1. Institute of Mathematics, Polish Academy of Sciences, Św. Tomasza 30/7, 31-027 Krakow, Poland, e-mail: napeszat@cyf-kr.edu.pl, , , , , , PL

    Szymon Peszat

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  1. Szymon Peszat
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Peszat, S. The Cauchy problem for a nonlinear stochastic wave equation in any dimension. J.evol.equ. 2, 383–394 (2002). https://doi.org/10.1007/PL00013197

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  • DOI: https://doi.org/10.1007/PL00013197

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