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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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Volume 25, Issue 5


Splitting-up scheme for nonlinear stochastic hyperbolic equations

Mamadou Sango
Published Online: 2011-07-19 | DOI: https://doi.org/10.1515/form.2011.138


In the present paper we develop the splitting-up scheme (so-called method of fractional steps) for the investigation of existence problem for a class of nonlinear hyperbolic equations containing some nonlinear terms which do not satisfy the Lipschitz condition. Through a careful blending of the numerical scheme and deep compactness results of both analytic and probabilistic nature we establish the existence of a weak probabilistic solution for the problem. Our work is the stochastic counterpart of some important results of Roger Temam obtained in the late sixties of the last century in his works on the development of the splitting-up method for deterministic evolution problems.

Keywords: Splitting-up scheme; hyperbolic stochastic equations; weak solutions; tightness of probability measures; compactness method

About the article

Received: 2009-11-10

Revised: 2011-03-16

Published Online: 2011-07-19

Published in Print: 2013-09-01

Citation Information: Forum Mathematicum, Volume 25, Issue 5, Pages 931–965, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.138.

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