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Numerical Experiments on a Nonlinear Wave Equation with Singular Solutions

  • Thomas HagstromEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 119)

Abstract

We use a Fourier pseudospectral method to compute solutions to the Cauchy problem for a nonlinear variational wave equation originally proposed as a model for the dynamics of nematic liquid crystals. The solution is known to form singularities in finite time; in particular space and time derivatives become unbounded. Beyond the singularity time, both conservative and dissipative Hölder continuous weak solutions exist. We present results with energy-conserving discretizations as well as with a vanishing viscosity sequence, noting marked differences between the computed solutions after the solution loses regularity.

Notes

Acknowledgements

This work was supported in part by NSF Grant DMS-1418871. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. We also acknowledge the use of FFT routines adapted from [7] as well as OpenMP-enabled FFTs adapted from [16] and written by Burkardt [5].

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Southern Methodist UniversityDallasUSA

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