Unique Solvability and Decomposition Method for One Nonlinear Multi-Dimensional Integro-Differential Parabolic Equation

Abstract

The paper is devoted to the construction and study of the decomposition type semi-discrete scheme for one nonlinear multi-dimensional integro-differential equation of parabolic type. Unique solvability of the first type initial-boundary value problem is given as well. The studied equation is some generalization of integro-differential model, which is based on the well-known Maxwell system arising in mathematical simulation of electromagnetic field penetration into a medium.