Newton’s method for nonlinear stochastic wave equations

We consider nonlinear stochastic wave equations driven by time-space white noise. The existence of solutions is proved by the method of successive approximations. Next we apply Newton’s method. The main result concerning its first-order convergence is based on Cairoli’s maximal inequalities for two-...

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Bibliographic Details
Published inForum mathematicum Vol. 32; no. 3; pp. 595 - 605
Main Authors Leszczyński, Henryk, Wrzosek, Monika
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.05.2020
Walter de Gruyter GmbH
Subjects
35R10
35R60
60H15
Approximation
Cairoli’s maximal inequality
Convergence
Martingales
Mathematical analysis
Newton’s method
nonlocal dependence
probabilistic convergence
wave equation
Wave equations
White noise
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Summary:We consider nonlinear stochastic wave equations driven by time-space white noise. The existence of solutions is proved by the method of successive approximations. Next we apply Newton’s method. The main result concerning its first-order convergence is based on Cairoli’s maximal inequalities for two-parameter martingales. Moreover, a second-order convergence in a probabilistic sense is demonstrated.
ISSN:0933-7741
1435-5337
DOI:10.1515/forum-2019-0090