Overdetermined Elliptic Systems
Foundations of Computational Mathematics
Involutive upgrades of Navier-Stokes solvers
International Journal of Computational Fluid Dynamics
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In this paper we apply methods of commutative algebra to analysis of systems of PDEs. More precisely, we show that systems which are parabolic in a generalized sense are equivalent to certain completed systems which are parabolic in the standard sense. We also propose a constructive method for getting this completion, and Grobner basis methods, via symbol modules of the systems, play a central role in practical computations. Moreover, we can easily construct systems which are not parabolic in the generalized sense but nevertheless become parabolic when completed.