Well-posedness and large deviations of Lévy-driven Marcus stochastic Landau-Lifshitz-Baryakhtar equation

2024/08/11 by Fan Xu, Bin Liu, Xu, Fan +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2408.05684

openalex publication_date 2024/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 H_\textrmeff influenced by external random noise. Under the natural assumption that the magnetic body O⊂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 ℍ¹(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.

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