Strong solutions to a nonlinear stochastic Maxwell equation with a retarded material law

Hornung, Luca

doi:10.48550/arxiv.1703.04461

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2019

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“…The well-posedness of stochastic Maxwell equations has been investigated by semigroup approach in [3,9], by a refined Faedo-Galerkin method and spectral multiplier theorem in [8], by using the stochastically perturbed PDEs approach in [10]. The regularity of the solution of stochastic Maxwell equations driven by Itô multiplicative noise is considered in [3], allowing sufficient spatial smoothness on the coefficients and noise term.…”

Section: Introductionmentioning

confidence: 99%

Runge--Kutta Semidiscretizations for Stochastic Maxwell Equations with Additive Noise

Chen¹,

Hong²,

Ji³

2019

SIAM J. Numer. Anal.

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The paper concerns semidiscretizations in time of stochastic Maxwell equations driven by additive noise. We show that the equations admit physical properties and mathematical structures, including regularity, energy and divergence evolution laws, and stochastic symplecticity, etc. In order to inherit the intrinsic properties of the original system, we introduce a general class of stochastic Runge-Kutta methods, and deduce the condition of symplecticity-preserving. By utilizing a priori estimates on numerical approximations and semigroup approach, we show that the methods, which are algebraically stable and coercive, are well-posed and convergent with order one in mean-square sense, which answers an open problem in [2] for stochastic Maxwell equations driven by additive noise.

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