On the Coalgebra of Partial Differential Equations
On the Coalgebra of Partial Differential Equations
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.
- University of Florence Italy
- Schloss Dagstuhl – Leibniz Center for Informatics Germany
- Leibniz Association Germany
polynomials, partial differential equations, Coalgebra; Partial differential equations; Polynomials, coalgebra, 004, ddc: ddc:004
polynomials, partial differential equations, Coalgebra; Partial differential equations; Polynomials, coalgebra, 004, ddc: ddc:004
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!