Invariant solutions of the normal hyperbolic mean curvature flow with dissipation. (English) Zbl 1439.35143
Summary: 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.
MSC:
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
| 35E05 | Fundamental solutions to PDEs and systems of PDEs with constant coefficients |
| 43A80 | Analysis on other specific Lie groups |
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