Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion

Henryk Leszczyński; Monika Wrzosek

doi:10.3934/mbe.2017015

Article Contents

2017, Volume 14, Issue 1: 237-248. Doi: 10.3934/mbe.2017015

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Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion

Henryk Leszczyński and
Monika Wrzosek

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

Author Bio: E-mail address: hleszcz@mat.ug.edu.pl; E-mail address: mwrzosek@mat.ug.edu.pl

Received: October 28, 2015

Accepted: April 11, 2016

Published: September 2017

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Abstract

We consider nonlinear stochastic wave equations driven by one-dimensional white noise with respect to time. The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.

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Mathematics Subject Classification: Primary: 60H15; Secondary: 35R60.

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