Martingale Solutions of Stochastic Constrained Modified Swift-Hohenberg Equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916719223635968 |
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| author | Ahmed, Saeed Hussain, Javed |
| author_facet | Ahmed, Saeed Hussain, Javed |
| contents | In this paper, we aim to prove the existence of global Martingale solution to Stochastic Constrained Modified Swift-Hohenberg Equation driven by stratonovich multiplicative noise. This equation belongs to class of amplitude equations which describe the appearance of pattern formation in nature. This structure allows us to work in a Hilbert space framework and to apply a stochastic Galerkin method. The existence proof is based on energy-type estimates, the tightness criterion of Brzezniak and collaborators, and Jakubowski's generalization of the Skorokhod theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01720 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Martingale Solutions of Stochastic Constrained Modified Swift-Hohenberg Equation Ahmed, Saeed Hussain, Javed Probability Analysis of PDEs In this paper, we aim to prove the existence of global Martingale solution to Stochastic Constrained Modified Swift-Hohenberg Equation driven by stratonovich multiplicative noise. This equation belongs to class of amplitude equations which describe the appearance of pattern formation in nature. This structure allows us to work in a Hilbert space framework and to apply a stochastic Galerkin method. The existence proof is based on energy-type estimates, the tightness criterion of Brzezniak and collaborators, and Jakubowski's generalization of the Skorokhod theorem. |
| title | Martingale Solutions of Stochastic Constrained Modified Swift-Hohenberg Equation |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2505.01720 |