On checking existence of infinitely differentiable solutions of partial differential equations with boundary conditions |
| |
Authors: | S V Paramonov |
| |
Affiliation: | 1.Department of Computational Mathematics and Cybernetics,Moscow State University,Moscow,Russia |
| |
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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |