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Splitting-up scheme for nonlinear stochastic hyperbolic equations
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Mamadou Sango
Published/Copyright:
July 19, 2011
Abstract.
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
Received: 2009-11-10
Revised: 2011-03-16
Published Online: 2011-07-19
Published in Print: 2013-09-01
© 2013 by Walter de Gruyter Berlin Boston
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Keywords for this article
Splitting-up scheme;
hyperbolic stochastic equations;
weak
solutions;
tightness of probability measures;
compactness method
Articles in the same Issue
- Masthead
- Morrey regularity for almost minimizers of asymptotically convex functionals with nonstandard growth
- Splitting-up scheme for nonlinear stochastic hyperbolic equations
- Pcf and abelian groups
- Cropping Euler factors of modular L-functions
- Maslov index, lagrangians, mapping class groups and TQFT
- Erratum [0.1mm] Use of reproducing kernels and Berezin symbols technique in some questions of operator theory [Forum Math., DOI 10.1515/FORM.2011.073]
