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oai:drops-oai.dagstuhl.de:10968 2024-03-06T10:46:56Z ddc:004 open_access

On the Coalgebra of Partial Differential Equations Boreale, Michele coalgebra partial differential equations polynomials 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Michele Boreale 2019 Is Part Of LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2019.24 urn:nbn:de:0030-drops-109689 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.24 eng https://creativecommons.org/licenses/by/3.0/legalcode