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BLOW-UP OF THE NONEQUIVARIANT ($2+1$)-DIMENSIONAL WAVE MAP

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Numerical problems in dynamical systems Hyperbolic equations and systems

Published online by Cambridge University Press:  18 March 2014

JÖRG FRAUENDIENER  and
RALF PETER
JÖRG FRAUENDIENER*
Affiliation:
Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand email rpeter@maths.otago.ac.nz
RALF PETER
Affiliation:
Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin 9054, New Zealand email rpeter@maths.otago.ac.nz
*
✉joergf@maths.otago.ac.nz
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Abstract

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It has been known for a long time that the equivariant $2+1$ wave map into the $2$-sphere blows up if the initial data are chosen appropriately. Here, we present numerical evidence for the stability of the blow-up phenomenon under explicit violations of equivariance.

Keywords

wave mapblow-upequivariancesymplectic integrator

MSC classification

Secondary: 35L53: Initial-boundary value problems for second-order hyperbolic systems 65M20: Method of lines 65P10: Hamiltonian systems including symplectic integrators
Type
Research Article
Information
The ANZIAM Journal , Volume 55 , Issue 2 , October 2013 , pp. 151 - 161
Copyright
Copyright © 2014 Australian Mathematical Society 

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