We study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of ultradifferentiable functions of class (M_p). We show that evolution is equivalent to the validity of a Phragmen-Lindeloef principle for entire and plurisubharmonic functions on some irreducible affine algebraic varieties. We find necessary and sufficient conditions for well-posedness and relate the hyperbolicity of a given system to that of its principal part.
Overdetermined differential systems in spaces of (small) Gevrey functions
BOITI, Chiara;
1999
Abstract
We study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of ultradifferentiable functions of class (M_p). We show that evolution is equivalent to the validity of a Phragmen-Lindeloef principle for entire and plurisubharmonic functions on some irreducible affine algebraic varieties. We find necessary and sufficient conditions for well-posedness and relate the hyperbolicity of a given system to that of its principal part.File in questo prodotto:
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