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Symmetries and conservation laws associated with a hyperbolic mean curvature flow

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Abstract

Under investigation in this paper is a hyperbolic mean curvature flow for convex evolving curves. Firstly, in view of Lie group analysis, infinitesimal generators, symmetry groups and an optimal system of symmetries of the considered hyperbolic mean curvature flow are presented. At the same time, some group invariant solutions are computed through reduced equations. In particular, we construct explicit solutions by applying the power series method. Furthermore, the convergence of the solutions of power series is certificated. Finally, conservation laws of the hyperbolic mean curvature flow are established via Ibragimov’s approach.

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Acknowledgement

The authors thank Professor Dexing Kong for his wonderful discussion.

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Authors and Affiliations

  1. College of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, China

    Ben Gao & Qing-lian Yin

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  1. Ben Gao
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  2. Qing-lian Yin
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Correspondence to Ben Gao.

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Supported by the Natural Science Foundation of Shanxi (202103021224068).

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Gao, B., Yin, Ql. Symmetries and conservation laws associated with a hyperbolic mean curvature flow. Appl. Math. J. Chin. Univ. 37, 583–597 (2022). https://doi.org/10.1007/s11766-022-4311-2

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  • DOI: https://doi.org/10.1007/s11766-022-4311-2

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