Finite-time blow-up in dynamical systems

doi:10.1016/S0375-9601(98)00822-6

Physics Letters A

Volume 250, Issues 4–6, 28 December 1998, Pages 311-318

https://doi.org/10.1016/S0375-9601(98)00822-6 Get rights and content

Abstract

A new method to detect finite-time blow-up in systems of ordinary differential equations is presented. This simple algorithmic procedure is based on the analysis of singularities in complex time and amounts to checking the real-valuedness of the leading order term in the asymptotic series describing the behavior of the general solution around movable singularities. Illustrative examples and an application to a magneto-hydrodynamic problem are given.

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Finite-time blow-up in dynamical systems

Abstract

J. Diff. Eq.

Phys. Lett. A

Phys. Rep.

Physica D

Invent. Math.

Physica D

Commum. Math. Phys.

Ann. Inst. Henri Poincaré

Arc. Rational Mech. Anal.

Commun. Pure and Appl. Math.

J. Math. Phys.

Necessary and sufficient conditions for finite time singularities in ordinary differential equations

J. Diff. Eq.

J. Fluid. Mech.

Phys. Rev. A

J. Physique

J. Phys. Soc. Jpn

Geophys. Astrophys. Fluid Dynamics