Well-posedness and large deviations of Lévy-driven Marcus stochastic Landau-Lifshitz-Baryakhtar equation
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909284455940096 |
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| author | Xu, Fan Liu, Bin Zhang, Lei |
| author_facet | Xu, Fan Liu, Bin Zhang, Lei |
| contents | This paper considers the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with pure jump noise in Marcus canonical form, which describes the dynamics of magnetic spin field in a ferromagnet at elevated temperatures with the effective field $\mathbf{H}_{\textrm{eff}}$ influenced by external random noise. Under the natural assumption that the magnetic body $\mathcal{O}\subset\mathbb{R}^d$ ($d=1,2,3$) is bounded with smooth boundary, we shall prove that the initial-boundary value problem of SLLBar equation possesses a unique global probabilistically strong and analytically weak solution with initial data in the energy space $\mathbb{H}^1(\mathcal{O})$. Then by employing the weak convergence method, we proceed to establish a Freidlin-Wentzell type large deviation principle for pathwise solutions to the SLLBar equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05684 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness and large deviations of Lévy-driven Marcus stochastic Landau-Lifshitz-Baryakhtar equation Xu, Fan Liu, Bin Zhang, Lei Analysis of PDEs Probability This paper considers the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with pure jump noise in Marcus canonical form, which describes the dynamics of magnetic spin field in a ferromagnet at elevated temperatures with the effective field $\mathbf{H}_{\textrm{eff}}$ influenced by external random noise. Under the natural assumption that the magnetic body $\mathcal{O}\subset\mathbb{R}^d$ ($d=1,2,3$) is bounded with smooth boundary, we shall prove that the initial-boundary value problem of SLLBar equation possesses a unique global probabilistically strong and analytically weak solution with initial data in the energy space $\mathbb{H}^1(\mathcal{O})$. Then by employing the weak convergence method, we proceed to establish a Freidlin-Wentzell type large deviation principle for pathwise solutions to the SLLBar equation. |
| title | Well-posedness and large deviations of Lévy-driven Marcus stochastic Landau-Lifshitz-Baryakhtar equation |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2408.05684 |