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. In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed. 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.
Sergei Igorevich Piskarev is an expert in the theory of semigroups of operators, cosine operator-function theory, differential equations in Banach spaces, numerical analysis in linear and semilinear differential equations in abstract spaces, ill-posed problems and approximation of the spectrum of operators. S Piskarev is the author or co-author of more than 100 research papers and communications in scientific journals, conference proceedings and special issues. S Piskarev is a participant and speaker of many international conferences on the subject on semigroups of operators and evolution equations and their approximations. S Piskarev is a lecturer in courses on basic mathematics for undergraduate students. Currently, he is a leading researcher of the Research Computing Center of the M V Lomonosov Moscow State University and the Russian Institute of Scientific and Technical Information of the Russian Academy of Sciences and a professor of the Mari State University and a professor of Mari State University and the Bauman Moscow State Technical University.
Alexey Vital'evich Ovchinnikov is a specialist in geometric and algebraic methods in nonlinear differential equations and optimal control theory. A Ovchinnikov is the author of several basic textbooks in mathematics for physics students and the co-author of monographs on the nonlinear mathematical physics (together with M Korpusov et al.). Currently, he is an assistant professor of the Faculty of Physics at the M V Lomonosov Moscow State University and the head of the Mathematical Department of the Russian Institute of Scientific and Technical Information of the Russian Academy of Sciences. A Ovchinnikov is an author and lecturer in courses on basic mathematics for undergraduate students. Also, he is a member of the Editorial board of the Journal of Mathematical Sciences (Springer) and a deputy editor-in-chief of the series Itogi Nauki i Tekhniki. Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory (Progress in Science and Technology. Contemporary Mathematicsa and Its Applications. Thematic Surveys) published by the Russian Institute of Scientific and Technical Information of the Russian Academy of Sciences.
