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On invariant subspaces for nonlinear finite-difference operators

Published online by Cambridge University Press:  14 November 2011

Victor A. Galaktionov
Victor A. Galaktionov
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, U.K. and Keldysh Institute of Applied Mathematics, Miusskaya Sq., 4, 125047 Moscow, Russia e-mail: [email protected]
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Extract

We study linear subspaces invariant under discrete operators corresponding to finitedifference approximations of differential operators with polynomial nonlinearities. In several cases, we establish a certain structural stability of invariant subspaces and sets of nonlinear differential operators of reaction–diffusion type with respect to their spatial discretisation. The corresponding lower-dimensional reductions of the finite-difference solutions on the invariant subspaces are constructed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 6 , 1998 , pp. 1293 - 1308
Copyright
Copyright © Royal Society of Edinburgh 1998

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