Well-posedness and large deviations of L\'{e}vy-driven Marcus stochastic Landau-Lifshitz-Baryakhtar equation

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 Heff influenced by external random noise. Under the natural assumption that the magnetic body Oᵈ ($d=1,2,3$) 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.