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On the Coalgebra of Partial Differential Equations

Author Michele Boreale



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Michele Boreale
  • Università di Firenze, Dipartimento di Statistica, Informatica, Applicazioni (DiSIA) "G. Parenti", Viale Morgagni 65, I-50134 Firenze, Italy

Acknowledgements

Three anonymous reviewers have provided valuable comments.

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Michele Boreale. On the Coalgebra of Partial Differential Equations. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 24:1-24:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.MFCS.2019.24

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Invariants
  • Theory of computation → Operational semantics
Keywords
  • coalgebra
  • partial differential equations
  • polynomials

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