The global behavior of solutions of evolution equations in noncylindrical domain with time-moving boundaries

时动边界非圆柱域演化方程解的全局行为

• 批准号: 15540213
• 负责人: YAMAGUCHI Masaru
• 金额: $ 2.3万
• 依托单位: Tokai University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540213/
• 关键词: nonlinear wave equation; Klein-Gordon equation; Suspended string equation; periodic solution; almost periodic solution; Diophantine approximation; cusp; Diophantine不等式; 重い振動弦の方程式; 重みをもつSobolev型空間; Schauderの不動点定理; 自由振動; Diophantine Condition

1) Let the space dimension be 1 to 5. Consider nonlinear sphere-symmetric autonomous wave equations in ball. We showed that the equations have infinitely many time-periodic solutions. In the proof we used the Diophantine inequalities on the eigenvalues of Laplacian and the periods. To this end we studied in detail numerical properties of the zero points of the Bessel functions, using the asymptotic expansions of the zero points.2) We considered IBVP for linear equations of heavy suspended string. Assume that time-quasiperiodic force works to the string. We assume the general Diophantine conditions on the eigenvalues of the string operator and the quasi perios Then we completely made clear the strunture of almost periodic structure of the solutions of IBVP. To show this statement, we defined well-matched function spaces, solved the eigenfunction problem in these function spaces and constructed the spectral theory.3) We considered BVP for nonlinear sphere-symmetric wave equations in ball with periodically moving boundaries. Then we showed the existence of periodic solutions of the BVP.4) The following theorem on the geodesics on manifolds is proved by M.Tanaka.Theorem : Let M be a real analytic Riemaniann manifold homeomorphic to a 2-sphere. If the Gaussian curvature of M is positive, then the conjugate locus of each point consists of a single point or has at least 4 cusps.

1）让空间维度为1至5。考虑球中的非线性球体对称自主波方程。我们表明这些方程具有无限的时间周期性解决方案。在证据中，我们在拉普拉斯（Laplacian）和时期的特征值上使用了七雄不平等。为此，我们使用零点的渐近扩展研究了贝塞尔函数的零点的数值特性。2）我们考虑了重型悬浮串的线性方程的IBVP。假设时间quasiperiodic力对字符串起作用。我们假设弦乐操作员和准杂烟草的特征值的一般性苯胺条件，然后我们完全明确了IBVP溶液的几乎周期性结构的解决方案。为了显示此陈述，我们定义了匹配良好的函数空间，解决了这些功能空间中的本亚函数问题，并构建了光谱理论。3）我们考虑了具有定期移动边界的球中非线性球形对称波方程的BVP。然后，我们展示了BVP的周期性解决方案的存在。4）M.Tanaka证明了关于歧管的大地测量学定理。Theorem：Let M成为2个角球的真实分析性Riemaniann歧管同源。如果M的高斯曲率为正，则每个点的共轭轨迹由单个点组成或至少具有4个尖端。

项目成果

Almost periodic oscillations of suspended string under quasiperiodic linearforce

准周期线性力作用下悬弦的近似周期振荡

• 发表时间: 2005
• 期刊: Journal of Mathematical Analysis and Applications vol 303-2
• 作者: M.Tanaka;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi
• 通讯作者: M.Yamaguchi

Free and forced vibrations of nonlinear wave equations in ball

• DOI: 10.1016/j.jde.2004.04.014
• 发表时间: 2004-09
• 期刊: Journal of Differential Equations
• 影响因子: 2.4
• 作者: M. Yamaguchi

Periodic solutions of nonlinear 3D WE in sphere-symmetric domain with periodically oscillating boundaries

具有周期性振荡边界的球对称域中非线性 3D WE 的周期解

• 发表时间: 2004
• 期刊: Progress in Analysis (Proc.of ISSAC Congress)
• 作者: M.Tanaka;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Tanaka;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi
• 通讯作者: M.Yamaguchi

Infinitely many periodic solutions of one-dimensional Klein Gordon equations

一维克莱因戈登方程的无穷多个周期解

• 发表时间: 2004
• 期刊: Mathematical Sciences and Applications 20
• 作者: M.Tanaka;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Tanaka;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi;M.Yamaguchi
• 通讯作者: M.Yamaguchi

Almost periodic oscillations of suspended string under quasiperiodic linear force

拟周期线性力作用下悬弦的近似周期振荡

• 发表时间: 2005
• 期刊: Journal of Mathematical Analysis and Applications Vol.303
• 作者: M.Tanaka;M.Yamaguchi;M.Yamaguchi
• 通讯作者: M.Yamaguchi