期刊论文详细信息
JOURNAL OF DIFFERENTIAL EQUATIONS 卷:261
The motion of closed hypersurfaces in the central force fields
Article
Yan, Weiping1 
[1] Xiamen Univ, Coll Math, Xiamen 361000, Peoples R China
关键词: Hyperbolic mean curvature flow;    Quasi-linear wave equation;    Smooth solution;    Nash-Moser iteration;    Stability;   
DOI  :  10.1016/j.jde.2016.04.020
来源: Elsevier
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【 摘 要 】

This paper studies the large time existence for the motion of closed hypersurfaces in a radially symmetric potential. Physically, this surface can be considered as an electrically charged membrane with a constant charge per area in a radially symmetric potential. The evolution of such surface has been investigated by Schnurer and Smoczyk [20]. To study its motion, we introduce a quasi-linear degenerate hyperbolic equation which describes the motion of the surfaces extrinsically. Our main results show the large time existence of such Cauchy problem and the stability with respect to small initial data. When the radially symmetric potential function v equivalent to 1, the local existence and stability results have been obtained by Notz [18]. The proof is based on a new Nash-Moser iteration scheme. (C) 2016 Elsevier Inc. All rights reserved.

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