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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.

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