Boundedness of the Domain of Definition is Undecidable for Polynomial ODEs

Consider the initial-value problem with computable parameters dx dt = p(t, x) x(t0) = x0, where p : Rn+1 Rn is a vector of polynomials and (t0, x0) Rn+1 . We show that the problem of determining whether the maximal interval of definition of this initial-value problem is bounded or not is in general undecidable.

• Type: Journal
• Year: 2008
• Where: ENTCS
• Authors: Daniel S. Graça, Jorge Buescu, Manuel Lameiras Campagnolo
• Keywords: Computable Parameters, Dx Dt, ENTCS 2008, Initial-value Problem