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Generalized flows and singular ODEs on differentiable manifolds

Generalized flows and singular ODEs on differentiable manifolds
Generalized flows and singular ODEs on differentiable manifolds
Based on the concept of manifold-valued generalized functions, we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right-hand sides in a global setting. After establishing several existence and uniqueness results for solutions of such equations and flows of singular vector fields, we compare the solution concept employed here with the purely distributional setting. Finally, we derive criteria securing that a sequence of smooth flows corresponding to the regularization of a given singular vector field converges to a measurable limiting flow.
generalized flows, singular odes on manifolds, manifold-valued generalized functions, colombeau generalized functions
0167-8019
221-241
Kunzinger, Michael
5ee9f681-a923-4fb5-b1c8-9454237dd721
Oberguggenberger, Michael
45e9aedf-938e-4c76-ada3-b6d16b49e89b
Steinbauer, Roland
053836b9-b9d0-4a1d-93b1-06500bc87b17
Vickers, James A.
719cd73f-c462-417d-a341-0b042db88634
Kunzinger, Michael
5ee9f681-a923-4fb5-b1c8-9454237dd721
Oberguggenberger, Michael
45e9aedf-938e-4c76-ada3-b6d16b49e89b
Steinbauer, Roland
053836b9-b9d0-4a1d-93b1-06500bc87b17
Vickers, James A.
719cd73f-c462-417d-a341-0b042db88634

Kunzinger, Michael, Oberguggenberger, Michael, Steinbauer, Roland and Vickers, James A. (2004) Generalized flows and singular ODEs on differentiable manifolds. Acta Applicandae Mathematicae, 80 (2), 221-241. (doi:10.1023/B:ACAP.0000013815.32211.24).

Record type: Article

Abstract

Based on the concept of manifold-valued generalized functions, we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right-hand sides in a global setting. After establishing several existence and uniqueness results for solutions of such equations and flows of singular vector fields, we compare the solution concept employed here with the purely distributional setting. Finally, we derive criteria securing that a sequence of smooth flows corresponding to the regularization of a given singular vector field converges to a measurable limiting flow.

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More information

Published date: January 2004
Keywords: generalized flows, singular odes on manifolds, manifold-valued generalized functions, colombeau generalized functions

Identifiers

Local EPrints ID: 29336
URI: http://eprints.soton.ac.uk/id/eprint/29336
ISSN: 0167-8019
PURE UUID: 031295db-3697-4513-b64d-86387cc688ca
ORCID for James A. Vickers: ORCID iD orcid.org/0000-0002-1531-6273

Catalogue record

Date deposited: 12 May 2006
Last modified: 09 Jan 2022 02:33

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Contributors

Author: Michael Kunzinger
Author: Michael Oberguggenberger
Author: Roland Steinbauer

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