License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2019.24
URN: urn:nbn:de:0030-drops-109689
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10968/
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Boreale, Michele

On the Coalgebra of Partial Differential Equations

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LIPIcs-MFCS-2019-24.pdf (0.5 MB)

Abstract

We note that the coalgebra of formal power series in commutative variables is final in a certain subclass of coalgebras. Moreover, a system Sigma of polynomial PDEs, under a coherence condition, naturally induces such a coalgebra over differential polynomial expressions. As a result, we obtain a clean coinductive proof of existence and uniqueness of solutions of initial value problems for PDEs. Based on this characterization, we give complete algorithms for checking equivalence of differential polynomial expressions, given Sigma.

BibTeX - Entry

@InProceedings{boreale:LIPIcs:2019:10968,
  author =	{Michele Boreale},
  title =	{{On the Coalgebra of Partial Differential Equations}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{24:1--24:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Peter Rossmanith and Pinar Heggernes and Joost-Pieter Katoen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10968},
  URN =		{urn:nbn:de:0030-drops-109689},
  doi =		{10.4230/LIPIcs.MFCS.2019.24},
  annote =	{Keywords: coalgebra, partial differential equations, polynomials}
}

Keywords: coalgebra, partial differential equations, polynomials
Collection: 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
Issue Date: 2019
Date of publication: 20.08.2019

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