Stochastic Landau–Lifshitz–Gilbert equation with anisotropy energy driven by pure jump noise

Brzeźniak, Zdzisław; Manna, Utpal

doi:10.1016/j.camwa.2018.08.009

Cited by 12 publications

(4 citation statements)

References 17 publications

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“…We again skip the proofs of the following result and refer the reader to [13], for example, for similar results. The reader can also refer to the preprints [15,25].…”

Section: Definition 33 (Aldous Conditionmentioning

confidence: 99%

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Relaxed optimal control for the stochastic Landau-Lifshitz-Bloch equation with jump noise

Gokhale

2023

Preprint

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We study the stochastic Landau-Lifshitz-Bloch equation perturbed by pure jump noise. In order to understand and also control the fluctuations and jumps observed in the hysteresis loop, we add noise and an external control to the effective field. We consider the control operator as one that can depend, even nonlinearly on both the control and the associated solution process. We reformulate the problem as a relaxed control problem by using random Young measures and show that the relaxed problem admits an optimal control. The proof employs the Aldous condition for establishing tightness of laws and a modified version of the Skorohod Theorem for obtaining subconvergence of laws.

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“…We again skip the proofs of the following result and refer the reader to [13], for example, for similar results. The reader can also refer to the preprints [15,25].…”

Section: Definition 33 (Aldous Conditionmentioning

confidence: 99%

“…[11,12], Motyl [39] depends on a deterministic compactness result, which further depends on some energy bounds and the Aldous condition-a stochastic variant of the Arzéla and Ascoli's equicontinuity result. A similar idea has been used in [13,14] for the stochastic LLG equation. We use the latter approach here.…”

Section: Soham Gokhalementioning

confidence: 99%

Relaxed optimal control for the stochastic Landau-Lifshitz-Bloch equation with jump noise

Gokhale

2023

Preprint

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“…Brzeźniak et al have studied in [4] the one-dimensional case and prove the large deviations principle to the SLLGEs for small noise asymptotic. Brzeźniak et al have proved in [6,7] existence of weak martingale solution for SLLGEs in three dimensions perturbed by jump noise in the Marcus canonical form with non-zero anisotropic energy E an , see [6] and non-zero exchange energy E ex only, see [7]. Recently, in [8,28], the authors have employed Wong-Zakai approximation technique to obtain the solvability and convergence of the time dependent transformed PDEs.…”

Section: Introductionmentioning

confidence: 99%

Wong–Zakai Approximation for Landau–Lifshitz–Gilbert Equation Driven by Geometric Rough Paths

2021

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We adapt Lyon’s rough path theory to study Landau–Lifshitz–Gilbert equations (LLGEs) driven by geometric rough paths in one dimension, with non-zero exchange energy only. We convert the LLGEs to a fully nonlinear time-dependent partial differential equation without rough paths term by a suitable transformation. Our point of interest is the regular approximation of the geometric rough path. We investigate the limit equation, the form of the correction term, and its convergence rate in controlled rough path spaces. The key ingredients for constructing the solution and its corresponding convergence results are the Doss–Sussmann transformation, maximal regularity property, and the geometric rough path theory.

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“…The approach from this paper is being currently applied by the first and third named authors and Utpal Manna to a study of the large deviation principle for 1-D stochastic Landau-Lifshitz equations, see [14]. In another directions, the first and third named authors and Martin Ondreját are a publication about the LDP for stochastic PDEs driven by infinite dimensional Lévy processes, see [17].…”

Section: Introductionmentioning

confidence: 99%

Well-posedness and large deviations for 2-D Stochastic Navier-Stokes equations with jumps

Brzeźniak¹,

Peng²,

Zhai³

2019

Preprint

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Under the classical local Lipschitz and one sided linear growth assumptions on the coefficients of the stochastic perturbations, we first prove the existence and the uniqueness of a strong (in both the probabilistic and PDEs sense) solution to the 2-D Stochastic Navier-Stokes equations driven by multiplicative Lévy noise. Applying the weak convergence method introduced by [19,18] for the case of the Poisson random measures, we establish a Freidlin-Wentzell type large deviation principle for the strong solution in PDE sense.

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Stochastic Landau–Lifshitz–Gilbert equation with anisotropy energy driven by pure jump noise

Cited by 12 publications

References 17 publications

Relaxed optimal control for the stochastic Landau-Lifshitz-Bloch equation with jump noise

Relaxed optimal control for the stochastic Landau-Lifshitz-Bloch equation with jump noise

Wong–Zakai Approximation for Landau–Lifshitz–Gilbert Equation Driven by Geometric Rough Paths

Well-posedness and large deviations for 2-D Stochastic Navier-Stokes equations with jumps

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