Global Strong Well-Posedness of the stochastic bidomain equations with FitzHugh-Nagumo transport
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866912247882711040 |
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| author | Hieber, Matthias Hussein, Amru Saal, Martin |
| author_facet | Hieber, Matthias Hussein, Amru Saal, Martin |
| contents | Consider the bidomain equations from electrophysiology with FitzHugh--Nagumo transport subject to current noise, i.e., subject to stochastic forcing modeled by a cylindrical Wiener process. It is shown that this set of equations admits a unique global, strong pathwise solution within the setting of critical spaces. The proof is based on combining methods from stochastic and deterministic maximal regularity. In addition, the method of extrapolation spaces from deterministic evolution equations is transferred to the stochastic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_03960 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Global Strong Well-Posedness of the stochastic bidomain equations with FitzHugh-Nagumo transport Hieber, Matthias Hussein, Amru Saal, Martin Probability Analysis of PDEs 60H15, 92C35, 35K65 (Primary) Consider the bidomain equations from electrophysiology with FitzHugh--Nagumo transport subject to current noise, i.e., subject to stochastic forcing modeled by a cylindrical Wiener process. It is shown that this set of equations admits a unique global, strong pathwise solution within the setting of critical spaces. The proof is based on combining methods from stochastic and deterministic maximal regularity. In addition, the method of extrapolation spaces from deterministic evolution equations is transferred to the stochastic setting. |
| title | Global Strong Well-Posedness of the stochastic bidomain equations with FitzHugh-Nagumo transport |
| topic | Probability Analysis of PDEs 60H15, 92C35, 35K65 (Primary) |
| url | https://arxiv.org/abs/2002.03960 |