A remark on triviality for the two-dimensional stochastic nonlinear wave equation

Oh T, Okamoto M, Robert T (2020)
STOCHASTIC PROCESSES AND THEIR APPLICATIONS 130(9): 5838-5864.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Oh, Tadahiro; Okamoto, Mamoru; Robert, TristanUniBi
Abstract / Bemerkung
We consider the two-dimensional stochastic damped nonlinear wave equation (SdNLW) with the cubic nonlinearity, forced by a space-time white noise. In particular, we investigate the limiting behavior of solutions to SdNLW with regularized noises and establish triviality results in the spirit of the work by Hairer et al. (2012). More precisely, without renormalization of the nonlinearity, we establish the following two limiting behaviors; (i) in the strong noise regime, we show that solutions to SdNLW with regularized noises tend to 0 as the regularization is removed and (ii) in the weak noise regime, we show that solutions to SdNLW with regularized noises converge to a solution to a deterministic damped nonlinear wave equation with an additional mass term. (C) 2020 The Author(s). Published by Elsevier B.V.
Stichworte
Nonlinear wave equation; Stochastic nonlinear wave equation; Renormalization; Triviality
Erscheinungsjahr
2020
Zeitschriftentitel
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
Band
130
Ausgabe
9
Seite(n)
5838-5864
ISSN
0304-4149
eISSN
1879-209X
Page URI
https://pub.uni-bielefeld.de/record/2945436

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Oh T, Okamoto M, Robert T. A remark on triviality for the two-dimensional stochastic nonlinear wave equation. STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 2020;130(9):5838-5864.
Oh, T., Okamoto, M., & Robert, T. (2020). A remark on triviality for the two-dimensional stochastic nonlinear wave equation. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 130(9), 5838-5864. doi:10.1016/j.spa.2020.05.010
Oh, T., Okamoto, M., and Robert, T. (2020). A remark on triviality for the two-dimensional stochastic nonlinear wave equation. STOCHASTIC PROCESSES AND THEIR APPLICATIONS 130, 5838-5864.
Oh, T., Okamoto, M., & Robert, T., 2020. A remark on triviality for the two-dimensional stochastic nonlinear wave equation. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 130(9), p 5838-5864.
T. Oh, M. Okamoto, and T. Robert, “A remark on triviality for the two-dimensional stochastic nonlinear wave equation”, STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 130, 2020, pp. 5838-5864.
Oh, T., Okamoto, M., Robert, T.: A remark on triviality for the two-dimensional stochastic nonlinear wave equation. STOCHASTIC PROCESSES AND THEIR APPLICATIONS. 130, 5838-5864 (2020).
Oh, Tadahiro, Okamoto, Mamoru, and Robert, Tristan. “A remark on triviality for the two-dimensional stochastic nonlinear wave equation”. STOCHASTIC PROCESSES AND THEIR APPLICATIONS 130.9 (2020): 5838-5864.

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