摘要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.
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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[2] Kong D X 2007 The Proceedings of ICCM 2007 (Beijing: Higher Educational Press) vol II p 95
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[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)
2011, Vol. 28 
