Generalized solutions to hyperbolic systems with random field coefficients
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913517895942144 |
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| author | Karakašević, Jelena Oberguggenberger, Michael Schwarz, Martin |
| author_facet | Karakašević, Jelena Oberguggenberger, Michael Schwarz, Martin |
| contents | The paper addresses linear hyperbolic systems in one space dimension with random field coefficients. In many applications, a low degree of regularity of the paths of the coefficients is required, which is not covered by classical stochastic analysis. For this reason, we place our analysis in the framework of Colombeau algebras of generalized functions. We obtain new characterizations of Colombeau stochastic processes and establish existence and uniqueness of solutions in this framework. A number of applications to stochastic wave and transport equations are given and the Colombeau solutions are related to classical weak solutions, when the latter exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17034 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized solutions to hyperbolic systems with random field coefficients Karakašević, Jelena Oberguggenberger, Michael Schwarz, Martin Probability Analysis of PDEs 35F40, 35R60 (Primary) 46F30, 60H15 (Secondary) The paper addresses linear hyperbolic systems in one space dimension with random field coefficients. In many applications, a low degree of regularity of the paths of the coefficients is required, which is not covered by classical stochastic analysis. For this reason, we place our analysis in the framework of Colombeau algebras of generalized functions. We obtain new characterizations of Colombeau stochastic processes and establish existence and uniqueness of solutions in this framework. A number of applications to stochastic wave and transport equations are given and the Colombeau solutions are related to classical weak solutions, when the latter exist. |
| title | Generalized solutions to hyperbolic systems with random field coefficients |
| topic | Probability Analysis of PDEs 35F40, 35R60 (Primary) 46F30, 60H15 (Secondary) |
| url | https://arxiv.org/abs/2409.17034 |