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About non-coincidence of invariant manifolds and intrinsic low dimensional manifolds (ILDM) by Sofia Borok; Igor Goldfarb; Vladimir Gol’dshtein is a Physics and Astronomy article available to read on EtoBox.

What is About non-coincidence of invariant manifolds and intrinsic low dimensional manifolds (ILDM) about?

The present paper contains an analysis of some aspects of a well known method of Intrinsic Low-Dimensional Manifolds (ILDM), which is regularly used for model reduction purposes in a number of combustion problems. One of these aspects relates to an existence of additional solutions (so-called ''ghost''-manifolds), which represent intrinsic low-dimensional manifolds and do NOT represent any slow invariant manifold even for two-dimensional singularly perturbed systems (for a small but finite singular parameter). These ''ghost''-manifolds are examples that contradict to the conjecture about the coincidence of ILDM and slow invariant manifolds published previously. Another aspect of the ILDM-method concerns the so-called transition zones (turning manifolds) between different invariant manifolds. It is shown that transition manifolds can not be correctly described by the ILDM-method. This statement is illustrated by an example taken from the mathematical theory of combustion.

Who reads About non-coincidence of invariant manifolds and intrinsic low dimensional manifolds (ILDM)?

Author

Sofia Borok; Igor Goldfarb; Vladimir Gol’dshtein

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 1007-5704)

Published

2008

Language

EN

Field

Physics and Astronomy (Physical Sciences)