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}
}
Comments
31 pages