On Some Nonlinear Partial Differential and Integro-Differential Diffusion Models

摘要

Existence, uniqueness, long-time behavior of solutions and algorithm of numerical resolution of initial-boundary value problem for one integro-differential system are studied. Attention is paid to construction and analysis of decomposition algorithms with respect to physical processes for one-dimensional nonlinear partial differential model based on Maxwell's system. Semi-discrete averaged models are constructed and investigated for this system. Finite difference schemes are studied. Investigated systems arise in modeling of process of the penetration of a magnetic field in a substance.