Stochastic integrodifferential equations in Hilbert spaces with applications in electromagnetics
Konstantinos B. Liaskos, Ioannis G. Stratis, Athanasios N. Yannacopoulos · Journal of Integral Equations and Applications · 2010
In this work we present some results on deterministic and stochastic integrodifferential equations in Hilbert spaces, motivated from and applied to problems arising from the mathematical modeling of electromagnetics fields in complex random media. We examine the mild, strong and classical well posedness for the Cauchy problem of the integrodifferential equation which describes Maxwell’s equations complemented with the general (and therefore nonlocal in time) linear constitutive relations describing such media, with either additive or multiplicative noise.