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

## TL;DR

This paper establishes existence and uniqueness of strong solutions for a nonlinear stochastic Maxwell equation with a retarded material law, employing advanced mathematical techniques like Faedo-Galerkin and spectral multiplier theorems.

## Contribution

It introduces a novel approach combining rescaling and spectral analysis to handle the stochastic Maxwell equation with complex nonlinear and retarded effects.

## Key findings

- Proved existence and uniqueness of strong solutions.
- Developed a refined Faedo-Galerkin method for this class of equations.
- Applied spectral multiplier theorems to obtain a priori estimates.

## 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.