AG 1, AG 2, AG 3, AG 4, AG 5, SWS, RG1, MMCI   Info

Public Audience

English

60 Minutes

Saarbrücken

We describe a combined algebraic and geometric framework to study singularities of implicit differential equations, i.e. equations which are not solved for their leading derivatives. At such singularities the traditional theory of differential equations is no longer valid and many new phenomena may appear: solutions may suddenly begin or end without apparent reason, finitely or even infinitely many solutions may exist for given initial data or solutions may be only of finite regularity even for analytic equations. We show how singularities can be algorithmically detected and classified in the complex case using the Thomas decomposition. For real differential equations, as they prevail in applications, this task leads to questions in real algebraic geometry which can be tackled with tools like cylindrical algebraic decompositions.

Jennifer Müller

2900

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