eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-08-20
24:1
24:13
10.4230/LIPIcs.MFCS.2019.24
article
On the Coalgebra of Partial Differential Equations
Boreale, Michele
1
Università di Firenze, Dipartimento di Statistica, Informatica, Applicazioni (DiSIA) "G. Parenti", Viale Morgagni 65, I-50134 Firenze, Italy
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol138-mfcs2019/LIPIcs.MFCS.2019.24/LIPIcs.MFCS.2019.24.pdf
coalgebra
partial differential equations
polynomials