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Terence Jegaraj - One of the best experts on this subject based on the ideXlab platform.

  • large deviations and transitions between equilibria for stochastic landau lifshitz gilbert equation
    Archive for Rational Mechanics and Analysis, 2017
    Co-Authors: Zdzislaw Brzeźniak, Beniamin Goldys, Terence Jegaraj
    Abstract:

    We study a stochastic Landau–Lifshitz equation on a bounded interval and with finite dimensional noise. We first show that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal Regularity Property. Next, we prove the large deviations principle for the small noise asymptotic of solutions using the weak convergence method. An essential ingredient of the proof is the compactness, or weak to strong continuity, of the solution map for a deterministic Landau–Lifschitz equation when considered as a transformation of external fields. We then apply this large deviations principle to show that small noise can cause magnetisation reversal. We also show the importance of the shape anisotropy parameter for reducing the disturbance of the solution caused by small noise. The problem is motivated by applications from ferromagnetic nanowires to the fabrication of magnetic memories.

  • large deviations and transitions between equilibria for stochastic landau lifshitz gilbert equation
    arXiv: Probability, 2012
    Co-Authors: Zdzislaw Brzeźniak, Beniamin Goldys, Terence Jegaraj
    Abstract:

    We study a stochastic Landau-Lifshitz equation on a bounded interval and with finite dimensional noise. We first show that there exists a pathwise unique solution to this equation and that this solution enjoys the maximal Regularity Property. Next, we prove the large deviations principle for small noise asymptotic of solutions using the weak convergence method. An essential ingredient of the proof is compactness, or weak to strong continuity, of the solution map for a deterministic Landau-Lifschitz equation, when considered as a transformation of external fields. We then apply this large deviations principle to show that small noise can cause magnetisation reversal. We also show the importance of the shape anisotropy parameter for reducing the disturbance of the solution caused by small noise. The problem is motivated by applications of ferromagnetic nanowires to the fabrication of magnetic memories. This is an updated version of the previous version of this paper.

Oscar Vegaamaya - One of the best experts on this subject based on the ideXlab platform.

Kai Liu - One of the best experts on this subject based on the ideXlab platform.

  • Hölder Continuous Regularity of Stochastic Convolutions with Distributed Delay
    Potential Analysis, 2021
    Co-Authors: Kai Liu
    Abstract:

    In this work, we consider the Hölder continuous Regularity of stochastic convolutions for a class of linear stochastic retarded functional differential equations with distributed delay in Hilbert spaces. By focusing on distributed delays, we first establish some more delicate estimates for fundamental solutions than those given in Liu (Discrete Contin. Dyn. Syst. Ser. B 25(4), 1279–1298, 2020 ). Then we apply these estimates to stochastic convolutions incurred by distributed delay to study their Regularity Property. Last, we present some easily-verified results by considering the Regularity of a class of systems whose delay operators have the same order derivatives as those in instantaneous ones.

  • on Regularity Property of retarded ornstein uhlenbeck processes in hilbert spaces
    Journal of Theoretical Probability, 2012
    Co-Authors: Kai Liu
    Abstract:

    In this work, some Regularity properties of mild solutions for a class of stochastic linear functional differential equations driven by infinite-dimensional Wiener processes are considered. In terms of retarded fundamental solutions, we introduce a class of stochastic convolutions which naturally arise in the solutions and investigate their Yosida approximants. By means of the retarded fundamental solutions, we find conditions under which each mild solution permits a continuous modification. With the aid of Yosida approximation, we study two kinds of Regularity properties, temporal and spatial ones, for the retarded solution processes. By employing a factorization method, we establish a retarded version of the Burkholder–Davis–Gundy inequality for stochastic convolutions.

  • on Regularity Property of retarded ornstein uhlenbeck processes in hilbert spaces
    arXiv: Probability, 2011
    Co-Authors: Kai Liu
    Abstract:

    In this work, some Regularity properties of mild solutions for a class of stochastic linear functional differential equations driven by infinite dimensional Wiener processes are considered. In terms of retarded fundamental solutions, we introduce a class of stochastic convolutions which naturally arise in the solutions and investigate their Yosida approximants. By means of the retarded fundamental solutions, we find conditions under which each mild solution permits a continuous modification. With the aid of Yosida approximation, we study two kinds of Regularity properties, temporal and spatial ones, for the retarded solution processes. By employing a factorization method, we establish a retarded version of Burkholder-Davis-Gundy's inequality for stochastic convolutions.

Maity Debayan - One of the best experts on this subject based on the ideXlab platform.

  • Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier-Stokes-Fourier fluid and a damped plate equation
    'Elsevier BV', 2021
    Co-Authors: Maity Debayan, Takahashi Takéo
    Abstract:

    International audienceThe article is devoted to the mathematical analysis of a fluid-structure interaction system where the fluid is compressible and heat conducting and where the structure is deformable and located on a part of the boundary of the fluid domain. The fluid motion is modeled by the compressible Navier-Stokes-Fourier system and the structure displacement is described by a structurally damped plate equation. Our main results are the existence of strong solutions in an $L^p-L^q$ setting for small time or for small data. Through a change of variables and a fixed point argument, the proof of the main results is mainly based on the maximal Regularity Property of the corresponding linear systems. For small time existence, this Property is obtained by decoupling the linear system into several standard linear systems whereas for global existence and for small data, the maximal Regularity Property is proved by showing that the corresponding linear coupled fluid-structure operator is R−sectorial

  • Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier-Stokes-Fourier fluid and a damped plate equation
    2020
    Co-Authors: Maity Debayan, Takahashi Takéo
    Abstract:

    The article is devoted to the mathematical analysis of a fluid-structure interaction system where the fluid is compressible and heat conducting and where the structure is deformable and located on a part of the boundary of the fluid domain. The fluid motion is modeled by the compressible Navier-Stokes-Fourier system and the structure displacement is described by a structurally damped plate equation. Our main results are the existence of strong solutions in an $L^p-L^q$ setting for small time or for small data. Through a change of variables and a fixed point argument, the proof of the main results is mainly based on the maximal Regularity Property of the corresponding linear systems. For small time existence, this Property is obtained by decoupling the linear system into several standard linear systems whereas for global existence and for small data, the maximal Regularity Property is proved by showing that the corresponding linear coupled {\em fluid-structure} operator is $\mathcal{R}-$sectorial

  • $L^p$-$L^q$ Maximal Regularity for some Operators associated with Linearized Incompressible Fluid-Rigid Body Problems
    'American Mathematical Society (AMS)', 2018
    Co-Authors: Maity Debayan, Tucsnak Marius
    Abstract:

    We study an unbounded operator arising naturally after linearizing the system modelling the motion of a rigid body in a viscous incompressible fluid. We show that this operator is $\mathcal{R}$ sectorial in $L^q$ for every $q \in (1,\infty)$, thus it has the maximal $L^p$-$L^q$ Regularity Property. Moreover, we show that the generated semigroup is exponentially stable with respect to the $L^q$ norm. Finally, we use these results to prove the global existence for small initial data, in an $L^p$-$L^q$ setting, for the original nonlinear problem

  • $L^p$-$L^q$ Maximal Regularity for some Operators Associated with Linearized Incompressible Fluid-Rigid Body Problems
    2017
    Co-Authors: Maity Debayan, Tucsnak Marius
    Abstract:

    We study an unbounded operator arising naturally after linearizing the system modelling the motion of a rigid body in a viscous incompressible fluid. We show that this operator is $\mathcal{R}$ sectorial in $L^q$ for every $q\in (1,\infty)$, thus it has the maximal $L^p$-$L^q$ Regularity Property. Moreover, we show that the generated semigroup is exponentially stable with respect to the $L^q$ norm. Finally, we use the results to prove the global existence for small initial data, in an $L^p$-$L^q$ setting, for the original nonlinear problem

Takahashi Takéo - One of the best experts on this subject based on the ideXlab platform.