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Large-time behaviour of solutions of the inviscid non-planar Burgers equation

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Abstract

Large-time behaviour of the entropy solution of an initial-value problem (IVP) for the inviscid non-planar Burgers equation is studied. The initial profile is assumed to be non-negative, bounded and compactly supported. The large-time behaviour of the support function of this entropy solution is also presented. This is achieved via the construction of the entropy solution of the IVP for the inviscid non-planar Burgers equation subject to the top-hat initial condition using the method of characteristics, Rankine–Hugoniot jump condition, and a similarity solution.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, India

    Ch. Srinivasa Rao & Manoj K. Yadav

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  1. Ch. Srinivasa Rao
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  2. Manoj K. Yadav
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Correspondence to Ch. Srinivasa Rao.

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Srinivasa Rao, C., Yadav, M.K. Large-time behaviour of solutions of the inviscid non-planar Burgers equation. J Eng Math 69, 345–357 (2011). https://doi.org/10.1007/s10665-010-9400-1

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  • DOI: https://doi.org/10.1007/s10665-010-9400-1

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