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On checking existence of infinitely differentiable solutions of partial differential equations with boundary conditions

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Abstract

The problem of checking existence of infinitely differentiable solutions of linear partial differential equations with zero boundary conditions is considered. The coefficients of the equations are assumed to be polynomials over Z in independent variables. It is proved that this problem is algorithmically undecidable. This result extends results of our earlier studies of analytic solutions. The proof relies on the result obtained by Denef and Lipshitz concerning the relationship between a certain subset of nonhomogeneous differential equations of the considered form (but without boundary conditions) and Diophantine equations.

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Authors and Affiliations

  1. Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia

    S. V. Paramonov

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  1. S. V. Paramonov
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Correspondence to S. V. Paramonov.

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Original Russian Text © S.V. Paramonov, 2016, published in Programmirovanie, 2016, Vol. 42, No. 2.

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Paramonov, S.V. On checking existence of infinitely differentiable solutions of partial differential equations with boundary conditions. Program Comput Soft 42, 107–111 (2016). https://doi.org/10.1134/S0361768816020079

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  • DOI: https://doi.org/10.1134/S0361768816020079

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