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Singularities in the geometric theory of differential equations

Pages: 784 - 793, Issue Special, September 2011

 Abstract        Full Text (1089.6K)              

Ulrike Kant - Institut für Mathematik, Universität Kassel, 34132 Kassel, Germany (email)
Werner M. Seiler - Institut für Mathematik, Universität Kassel, 34132 Kassel, Germany (email)

Abstract: We briefly recall the basic ideas of the Vessiot theory, a geometric approach to di fferential equations based on vector fields. Then we show that it allows to extend naturally some results on singularities for ordinary diff erential equations to maximally overdetermined partial diff erential equations.

Keywords:  Regular Singularities, irregular singularities, impasse points, singular integrals, Vessiot distribution, generalised solutions, Clairaut equations
Mathematics Subject Classification:  Primary: 35A30 Secondary: 34A09, 35A20, 35D99

Received: July 2010;      Revised: January 2011;      Published: October 2011.