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Numerical Simulation of Hyperbolic Gradient Flow with Pressure |
| LI Dong **, XIE Zheng, YI Dong-Yun
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| Department of Mathematics and Systems Science, National University of Defense Technology, Changsha 410073 |
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| Cite this article: |
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LI Dong, XIE Zheng, YI Dong-Yun 2011 Chin. Phys. Lett. 28 070203 |
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Abstract We propose a numerical algorithm for hyperbolic gradient flow with pressure for the initial value problem and boundary value problem on a compact manifold to investigate the influence of pressure on the evolution of the manifold. In particular, we simulate the behavior of a cotangent vector field on compact submanifolds in R3, and show that shock waves are generated.
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02.40.Vh
02.30.Jr
02.40.Ky
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Received: 24 April 2011
Published: 29 June 2011
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| PACS: |
02.40.Vh
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(Global analysis and analysis on manifolds)
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02.30.Jr
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(Partial differential equations)
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02.40.Ky
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(Riemannian geometries)
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[1] Dai W R, Kong D X and Liu K F 2008 Asian J. Math. 12 345
[2] Kong D X 2007 The Proceedings of ICCM 2007 (Beijing: Higher Educational Press) vol II p 95
[3] Kong D X and Liu K F 2007 J. Math. Phys. 48 103508
[4] Kong D X, Liu K F and Xu D L 2009 Commun. Part. Diff. Eq. 34 553
[5] Dai W R, Kong D X and Liu K F 2010 Pure and Applied Mathematics Quarterly 6 331
[6] Xie Z and Ye Z 2010 Pure and Applied Mathematics Quarterly (accepted)
[7] Kong D X and Liu K F arXiv:1009.3993v1
[8] Xie Z, Li D, Zhao Z Y and Wang Z L 2011 Pure and Applied Mathematics Quarterly (accepted)
[9] Desbrun M, Hirani A N, Leok M and Marsden J E arXiv:math/0508341v2
[10] Knobel R 2000 An Introduction to the Mathematical Theory of Waves (Providence: American Mathematical Society)
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