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Completion of overdetermined parabolic PDEs. (English) Zbl 1158.35393
Summary: 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 Gröbner 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.

MSC:
35N10 Overdetermined systems of PDEs with variable coefficients
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
68W30 Symbolic computation and algebraic computation
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