Abstract.
In this paper 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 Phragmén-Lindelöf principle for entire and plurisubharmonic functions on some irreducible affine algebraic varieties, and make applications in different situations. We find necessary and sufficient conditions for well posedness, and relate the hyperbolicity of a given system to that of its principal part.
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Received: January 19, 1999¶Published online: May 10, 2001
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Boiti, C., Nacinovich, M. The overdetermined Cauchy problem in some classes of ultradifferentiable functions. Annali di Matematica 180, 81–126 (2001). https://doi.org/10.1007/s10231-001-8199-9
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DOI: https://doi.org/10.1007/s10231-001-8199-9