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

Hornung, Luca

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.

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DOI: 10.5445/IR/1000067669
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2017
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000067669
Verlag KIT, Karlsruhe
Umfang 32 S.
Serie CRC 1173 ; 2017/6
Schlagworte stochastic Maxwell equations, Kerr-type nonlinearity, retarded material law, monotone coefficients, weak solutions, strong solutions, generalized Gaussian bounds, Hodge-Laplacian, spectral multiplier theorems, rescaling transformation
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