Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms.

*(English)*Zbl 07272910Summary: We study a level-set mean curvature flow equation with driving and source terms, and establish convergence results on the asymptotic behavior of solutions as time goes to infinity under some additional assumptions. We also study the associated stationary problem in details in a particular case, and establish Alexandrov’s theorem in two dimensions in the viscosity sense, which is of independent interest.

##### MSC:

35B40 | Asymptotic behavior of solutions to PDEs |

35K93 | Quasilinear parabolic equations with mean curvature operator |

35K20 | Initial-boundary value problems for second-order parabolic equations |

53E10 | Flows related to mean curvature |

##### Keywords:

asymptotic speed; birth and spread type nonlinear PDEs; fully nonlinear parabolic equations; forced mean curvature flow; crystal growth
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\textit{Y. Giga} et al., Discrete Contin. Dyn. Syst., Ser. B 25, No. 10, 3983--3999 (2020; Zbl 07272910)

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##### References:

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