黎曼流形中弹性线的运动与奇异摄动

IF 0.5 4区数学 Q3 MATHEMATICS

Osaka Journal of Mathematics Pub Date : 2015-04-01 DOI:10.18910/57640

N. Koiso

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引用次数: 2

摘要

R.E. Caflish和J.H. Maddocks分析了平面细长弹性杆的动力学。我们考虑一根n维黎曼流形中的细弹性杆。前一种模型表示一根具有正密度的弹性杆，方程变成半线性波动方程。我们的模型表示一根无限细的弹性杆，方程变成一维半线性方程。证明了解的短时间存在性。我们还讨论了阻力趋于无穷时的解的性质，并发现解收敛于梯度流动方程的解。

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ON MOTION OF AN ELASTIC WIRE IN A RIEMANNIAN MANIFOLD AND SINGULAR PERTURBATION

R.E. Caflish and J.H. Maddocks analyzed the dynamics of a plana r slender elastic rod. We consider a thin elastic rod in an N-dimensional riemannian manifold. The former model represents an elastic rod with positive thi ckness, and the equation becomes a semilinear wave equation. Our model represents an infinitely thin elastic rod, and the equation becomes a 1-dimensional semilinear pl ate equation. We prove the short time existence of solutions. We also discuss the be aviour of the solution when the resistance goes to infinity, and find that the solutio n converges to a solution of a gradient flow equation.

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来源期刊

Osaka Journal of Mathematics 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Osaka Journal of Mathematics is published quarterly by the joint editorship of the Department of Mathematics, Graduate School of Science, Osaka University, and the Department of Mathematics, Faculty of Science, Osaka City University and the Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University with the cooperation of the Department of Mathematical Sciences, Faculty of Engineering Science, Osaka University. The Journal is devoted entirely to the publication of original works in pure and applied mathematics.