Threshold of Singularity Formation in the Semilinear Wave Equation

Steven L. Liebling

doi:10.1103/PhysRevD.71.044019

Threshold of Singularity Formation in the Semilinear Wave Equation

General Relativity and Quantum Cosmology 2009-11-11 v1 Mathematical Physics math.MP

Authors: Steven L. Liebling

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Abstract

Solutions of the semilinear wave equation are found numerically in three spatial dimensions with no assumed symmetry using distributed adaptive mesh refinement. The threshold of singularity formation is studied for the two cases in which the exponent of the nonlinear term is either $p=5$ or $p=7$ . Near the threshold of singularity formation, numerical solutions suggest an approach to self-similarity for the $p=7$ case and an approach to a scale evolving static solution for $p=5$ .

Keywords

semilinear wave equation singularity formation threshold self-similarity adaptive mesh refinement three spatial dimensions

Cite

@article{arxiv.gr-qc/0502056,
  title  = {Threshold of Singularity Formation in the Semilinear Wave Equation},
  author = {Steven L. Liebling},
  journal= {arXiv preprint arXiv:gr-qc/0502056},
  year   = {2009}
}