Nonlinear stochastic wave equations

M. Oberguggenberger; F. Russo

doi:10.1080/10652469808819152

Nonlinear stochastic wave equations

M. Oberguggenberger, F. Russo

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is devoted to nonlinear stochastic wave equations with a globally Lipschitz nonlinearity and white noise excitation. We prove existence and uniqueness of generalized solutions, which are stochastic processes valued in the Colombeau algebra of generalized functions. In case the nonlinearity vanishes at infinity, we show that these solutions converge in probability to the distributional solutions of the linear equation.

Original language	English
Pages (from-to)	71-83
Number of pages	13
Journal	Integral Transforms and Special Functions
Volume	6
Issue number	1-4
DOIs	https://doi.org/10.1080/10652469808819152
Publication status	Published - 1 Jan 1998
Externally published	Yes

Keywords

Generalized functions
Nonlinear stochastic partial differential equations
Pathwise limits

Access to Document

10.1080/10652469808819152

Cite this

@article{98a667274ae642f19b7e75fec160ac89,

title = "Nonlinear stochastic wave equations",

abstract = "This paper is devoted to nonlinear stochastic wave equations with a globally Lipschitz nonlinearity and white noise excitation. We prove existence and uniqueness of generalized solutions, which are stochastic processes valued in the Colombeau algebra of generalized functions. In case the nonlinearity vanishes at infinity, we show that these solutions converge in probability to the distributional solutions of the linear equation.",

keywords = "Generalized functions, Nonlinear stochastic partial differential equations, Pathwise limits",

author = "M. Oberguggenberger and F. Russo",

year = "1998",

month = jan,

day = "1",

doi = "10.1080/10652469808819152",

language = "English",

volume = "6",

pages = "71--83",

journal = "Integral Transforms and Special Functions",

issn = "1065-2469",

number = "1-4",

}

TY - JOUR

T1 - Nonlinear stochastic wave equations

AU - Oberguggenberger, M.

AU - Russo, F.

PY - 1998/1/1

Y1 - 1998/1/1

N2 - This paper is devoted to nonlinear stochastic wave equations with a globally Lipschitz nonlinearity and white noise excitation. We prove existence and uniqueness of generalized solutions, which are stochastic processes valued in the Colombeau algebra of generalized functions. In case the nonlinearity vanishes at infinity, we show that these solutions converge in probability to the distributional solutions of the linear equation.

AB - This paper is devoted to nonlinear stochastic wave equations with a globally Lipschitz nonlinearity and white noise excitation. We prove existence and uniqueness of generalized solutions, which are stochastic processes valued in the Colombeau algebra of generalized functions. In case the nonlinearity vanishes at infinity, we show that these solutions converge in probability to the distributional solutions of the linear equation.

KW - Generalized functions

KW - Nonlinear stochastic partial differential equations

KW - Pathwise limits

U2 - 10.1080/10652469808819152

DO - 10.1080/10652469808819152

M3 - Article

AN - SCOPUS:0032251417

SN - 1065-2469

VL - 6

SP - 71

EP - 83

JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

IS - 1-4

ER -

Nonlinear stochastic wave equations

Abstract

Keywords

Access to Document

Fingerprint

Cite this