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Non-strictly Hyperbolic Systems, Singularity and Bifurcation

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Abstract

This paper examines the effect of non-strict hyperbolicity on singularity formation for a quasilinear 2\(\,\times \,\)2 system. We will show that for appropriate data a singularity can form solely along a curve in the (x, t) plane where strict hyperbolicty is lost. Furthermore, this curve may bifurcate at some point. Numerous examples are considered for Riemann and smooth data.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Loyola University, New Orleans, LA , 70118, USA

    Xuefeng Li & Katarzyna Saxton

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  1. Xuefeng Li
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  2. Katarzyna Saxton
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Correspondence to Katarzyna Saxton.

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Li, X., Saxton, K. Non-strictly Hyperbolic Systems, Singularity and Bifurcation. J Sci Comput 64, 696–720 (2015). https://doi.org/10.1007/s10915-014-9876-3

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  • DOI: https://doi.org/10.1007/s10915-014-9876-3

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