Abstract
In this paper, based on the classical Lie symmetry method, the group invariant solutions of the normal hyperbolic mean curvature flow with dissipation are discussed. The optimal system of the obtained symmetries is found, the reduced equations and exact solutions are investigated. Then explicit solutions are obtained by the power series method. In addition, the convergence of the power series solutions is proved. The objective shapes of the solutions of the normal hyperbolic mean curvature flow with dissipation are performed.
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Acknowledgements
The authors would like to thank Prof. De-Xing Kong for drawing our attention to the hyperbolic geometric flow. In addition, we are grateful to the referees for their constructive comments and suggestions, which have greatly improved this paper.
Funding
This research was supported by the Natural Science Foundation of Shanxi (No. 201801D121018).
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Gao, B., Shi, Z. Invariant solutions of the normal hyperbolic mean curvature flow with dissipation. Arch. Math. 114, 227–239 (2020). https://doi.org/10.1007/s00013-019-01397-4
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DOI: https://doi.org/10.1007/s00013-019-01397-4
Keywords
- Normal hyperbolic mean curvature flow with dissipation
- Symmetries
- Optimal system
- Power series solutions