Аннотация:The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems. We discuss and examine such concepts as abstract parabolic equations, general approximation schemes, compact convergence, attractors, unstable and stable manifolds, upper and lower semicontinuity of attractors, affinity principle, principle of compact approximation, semilinear differential equations in Banach spaces, periodic solutions of semilinear equations, stability of solution in Lyapunov’s sense, hyperbolic equilibrium points, semiflows, rotation of vector fields, index of a solution, shadowing, analytic C0-semigroups, Banach spaces, semidiscretization, discretization in space and in time, fractional equations, fractional powers of operators, condensing operators, etc. In this monograph, the most important and principal results scattered in many research papers are collected together and systemized. The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.
