Newton’s method for nonlinear stochastic wave equations-Reference-Cited by-同舟云学术

Newton’s method for nonlinear stochastic wave equations

Published:2020-02-11 Issue:3 Volume:32 Page:595-605
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Leszczyński Henryk¹,Wrzosek Monika¹

Affiliation:

1. Institute of Mathematics , University of Gdańsk , Wita Stwosza 57, 80-952 Gdańsk , Poland

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2019-0090/pdf

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