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


Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Somente assinantes

Resumo

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.

Sobre autores

S. Paramonov

Department of Computational Mathematics and Cybernetics

Autor responsável pela correspondência
Email: s.v.paramonov@yandex.ru
Rússia, Moscow, 119991

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML

Declaração de direitos autorais © Pleiades Publishing, Ltd., 2016