Acta Applicandae Mathematica

, Volume 80, Issue 2, pp 221–241

Generalized Flows and Singular ODEs on Differentiable Manifolds

  • Michael Kunzinger
  • Michael Oberguggenberger
  • Roland Steinbauer
  • James A. Vickers
Article
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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.

generalized flows singular ODEs on manifolds manifold-valued generalized functions Colombeau generalized functions 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Michael Kunzinger
  • Michael Oberguggenberger
  • Roland Steinbauer
  • James A. Vickers

There are no affiliations available

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