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

Probability 2017-03-14 v1

Abstract

We study the Cauchy problem for a semilinear stochastic Maxwell equation with Kerr-type nonlinearity and a retarded material law. We show existence and uniqueness of strong solutions using a refined Faedo-Galerkin method and spectral multiplier theorems for the Hodge-Laplacian. We also make use of a rescaling transformation that reduces the problem to an equation with additive noise to get an appropriate a priori estimate for the solution.

Keywords

Cite

@article{arxiv.1703.04461,
  title  = {Strong solutions to a nonlinear stochastic Maxwell equation with a retarded material law},
  author = {Luca Hornung},
  journal= {arXiv preprint arXiv:1703.04461},
  year   = {2017}
}

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31 pages