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Remarks on large time behavior of level-set mean curvature flow equations with driving and source terms. (English) Zbl 07272910
Summary: 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
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