Splitting-up scheme for nonlinear stochastic hyperbolic equations (Q2855505)
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scientific article; zbMATH DE number 6220098
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Splitting-up scheme for nonlinear stochastic hyperbolic equations |
scientific article; zbMATH DE number 6220098 |
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Splitting-up scheme for nonlinear stochastic hyperbolic equations (English)
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25 October 2013
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hyperbolic stochastic equations
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splitting-up scheme
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weak solutions
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tightness of probability measures
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compactness method
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Based on the author's abstract: In the present paper, the author develops a splitting-up scheme (so-called method of fractional steps) for the investigation of the 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, the existence of a weak probabilistic solution of the problem is established. This work is the stochastic counterpart of some important results of Roger Temam obtained in the late 1960s in his works on the development of the splitting-up method for deterministic evolution problems.
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