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
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
January 2004
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), .
(doi:10.1023/B:ACAP.0000013815.32211.24).
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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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
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Date deposited: 12 May 2006
Last modified: 16 Mar 2024 02:34
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Contributors
Author:
Michael Kunzinger
Author:
Michael Oberguggenberger
Author:
Roland Steinbauer
Author:
James A. Vickers
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