1. An orderly linear PDE system with analytic initial conditions with a non-analytic solution
- Author
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François Lemaire, Calcul Formel (CALFOR), Laboratoire d'Informatique Fondamentale de Lille (LIFL), Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS), Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS), and Lifl, Hal
- Subjects
[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC] ,Gevrey series ,Algebra and Number Theory ,Riquier–Janet ,Generalization ,[INFO.INFO-SC] Computer Science [cs]/Symbolic Computation [cs.SC] ,Mathematical analysis ,Order (ring theory) ,Differential algebra ,PDE ,Cauchy–Kovalevskaya theorem ,Computational Mathematics ,Characteristic sets ,Ranking ,Applied mathematics ,Analytic solution ,Mathematics - Abstract
Special Issue on Computer Algebra and Computer Analysis; International audience; We give a linear PDE system, with analytic initial conditions given w.r.t an orderly ranking, the solution of which is not analytic (moreover the solution is not Gevrey for any order). This examples proves that the analyticity Riquier theorem (generalization of the Cauchy-Kovalevskaya theorem) does not generalize to PDE systems endowed with orderly rankings.
- Published
- 2003
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