带有耗散项的双曲平均曲率流

Abstract

Abstract:

Hyperbolic mean curvature flow with a dissipative term is introduced. By a strick of DeTurk, the quasilinear hyperbolic equations can be reduced to the strictly hyperbolic equations. Local existence and uniqueness of the flow is proved. Furthermore, we discuss the nonlinear stability of the flow defined in $\mathbb{R}^{n}(n>2)$. Finally, the evolution equations of metric and curvature are derived.

Key words: hyperbolic mean curvature flow with a dissipative term, local existence, nonlinear stability, nonlinear wave equations

CLC Number:

O175.2

Zenggui Wang. Hyperbolic Mean Curvature Flow with A Dissipative Term[J].Acta mathematica scientia,Series A, 2026, 46(5): 1691-1705.

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References 46

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Hyperbolic Mean Curvature Flow with A Dissipative Term

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