The overdetermined Cauchy problem
Annales de l'Institut Fourier, Volume 47 (1997) no. 1, pp. 155-199.

We consider the (characteristic and non-characteristic) Cauchy problem for a system of constant coefficients partial differential equations with initial data on an affine subspace of arbitrary codimension. We show that evolution is equivalent to the validity of a principle on the complex characteristic variety and we study the relationship of this condition with the one introduced by Hörmander in the case of scalar operators and initial data on a hypersurface.

On considère le problème de Cauchy (caractéristique et non-caractéristique) pour les systèmes d’équations aux dérivées partielles à coefficients constants et données initiales sur un sous-espace affine de codimension arbitraire. On montre que l’évolution est équivalente à la validité d’un principe de Phragmén-Lindelöf sur la variété caractéristique complexe et on étudie ensuite la relation avec les conditions formulées par Hörmander dans le cas d’un opérateur scalaire et données sur une hypersurface.

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Boiti, Chiara; Nacinovich, Mauro. The overdetermined Cauchy problem. Annales de l'Institut Fourier, Volume 47 (1997) no. 1, pp. 155-199. doi : 10.5802/aif.1564. http://archive.numdam.org/articles/10.5802/aif.1564/

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