Abstract Semilinear Differential Equations
the Faculty of Physics of Lomonosov Moscow State University

Textbook:Attractors, Shadowing, and Approximation of Abstract Semilinear Differential Equations
Author(s): Sergey I Piskarev, Alexey V Ovchinnikov
M V Lomonosov Moscow State University

Course description:
This course discusses and examines 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, semidis-cretization, 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.