Geodesic
On a new approach to asymptotic stabilization problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 12, pp. 2167-2181

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A numerical algorithm for solving the asymptotic stabilization problem by the initial data to a fixed hyperbolic point with a given rate is proposed and justified. The stabilization problem is reduced to projecting the resolving operator of the given evolution process on a strongly stable manifold. This approach makes it possible to apply the results to a wide class of semidynamical systems including those corresponding to partial differential equations. By way of example, a numerical solution of the problem of the asymptotic stabilization of unstable trajectories of the two-dimensional Chafee–Infante equation in a circular domain by the boundary conditions is given. 
@article{ZVMMF_2009_49_12_a6,
     author = {A. A. Ivanchikov and A. A. Kornev and A. V. Ozeritskii},
     title = {On a~new approach to asymptotic stabilization problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2167--2181},
     publisher = {mathdoc},
     volume = {49},
     number = {12},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_12_a6/}
}
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A. A. Ivanchikov; A. A. Kornev; A. V. Ozeritskii. On a new approach to asymptotic stabilization problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 12, pp. 2167-2181. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_12_a6/