Boundedness of the Domain of Definition is Undecidable for Polynomial ODEs

  • Authors:
  • Daniel S. Graça;Jorge Buescu;Manuel L. Campagnolo

  • Affiliations:
  • DM/FCT, University of Algarve, Faro, Portugal and SQIG/IT Lisbon, Portugal;DM/FCUL, University of Lisbon, Portugal and CAMGSD, Lisbon, Portugal;DM/ISA, Technical University of Lisbon, Portugal and SQIG/IT Lisbon, Portugal

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2008

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Abstract

Consider the initial-value problem with computable parameters{dxdt=p(t,x)x(t"0)=x"0, where p:R^n^+^1-R^n is a vector of polynomials and (t"0,x"0)@?R^n^+^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.