Threshold of Singularity Formation in the Semilinear Wave Equation

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 $p=5$.

6 pages, 7 figures

References in corpus (4)

• The Singularity Threshold of the Nonlinear Sigma Model Using 3D Adaptive Mesh Refinement
• On blowup for Yang-Mills fields
• Singularity Formation in 2+1 Wave Maps
• The Nonlinear Sigma Model With Distributed Adaptive Mesh Refinement

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