Geodesic
Attractors, shadowing, and approximation of abstract semilinear differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Functional Analysis, Tome 189 (2021), pp. 3-130

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The review covers such sections of the theory of approximation of abstract differential equations as the approximation of attractors in the case of hyperbolic stationary points, the shadowing and, finally, the approximation of fractional in time semilinear problems.
Mots-clés : abstract parabolic equations
Keywords: general approximation scheme, compact convergence of resolvents, attractor, unstable manifold, stable manifold, upper and lower semicontinuity of attractors, affinity principle, principle of compact approximation, semilinear differential equation, Banach space, periodic solution, Lyapunov stability, hyperbolic equilibrium, semiflow, rotation of a vector field, index of a solution, shadowing, analytic $C_0$-semigroup, semidiscretization, discretization in space, discretization in time, fractional equation, fractional power of an operator, condensing operator. 
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     author = {S. I. Piskarev and A. V. Ovchinnikov},
     title = {Attractors, shadowing, and approximation of abstract semilinear differential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
     volume = {189},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_189_a0/}
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S. I. Piskarev; A. V. Ovchinnikov. Attractors, shadowing, and approximation of abstract semilinear differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Functional Analysis, Tome 189 (2021), pp. 3-130. http://geodesic.mathdoc.fr/item/INTO_2021_189_a0/