Studies on singular perturbation problems in nonlinear mechanics

非线性力学奇异摄动问题的研究

• 批准号: 11304005
• 负责人: OKAMOTO Hisashi
• 金额: $ 10.66万
• 依托单位: KYOTO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11304005/
• 关键词: singularity; blow-up of solutions; interior layer; self-similar solution; bifurcation; dynamical system; periodic solution; Navier-Stokes equations!; ナビエストークス方程式; ボルツマン方程式; 衝撃波; KdV方程式; 水面波; 渦力学; 反応拡散系

(1) New phenomena on the Navier-Stokes equations were found. Among others, solutions having interior layers and those solutions having k-10 spectra are remarkable. (2) Bifurcation phenomena in surface waves were clarified. In particular, an accurate numerical method was developed for singular solitary waves. (3) dynamical systems viewpoints on the shell model of turbulence proposed by Ohkitani and Yamada were enhanced. (4) applications to reaction-diffusion systems, (5) vortex formation in the 2-dimensional decaying turbulence by Y. Kimura. (6) asymptotic behavior of shock wave solutions was clarified by Kawashima and Matsumura.Okamoto, with the aid by Kim Sunchul, analyzed the bifurcating solutions arising in the rhombic periodic flows. It was demonstrated, by an elaborate numerical computations, that some solutions have k-10 spectra as the Reynolds number tends to infinity. Okamoto and A. Craik considered a three-dimensional dynamical system arising in fluid mechanics. Two different … More solutions, one with 90-degree bending and one without bending, were found and the mechanism of them was theoretically explained.Y. Kimura, with J. Herring, successfully explained theoretical background of vortex structures arising in rotating fluid. S. Kawashima proved the well-posedness of radiating gases.T. Ikeda considered models for combustion synthesis. With numerical experiments he demonstrated that the solutions of the model can reproduce the results of the laboratory experiments.H. Ikeda and H. Okamoto considered a special solution of the Navier-Stokes equations called Oseen flows. Some interior layers was rigorously proved. H. Ikeda also proved that a Hopf bifurcation occurs in the traveling wave solutions of a certain bi-stable system of reaction diffusion.H. Fujita proved the existence of the solutions of the Navier-Stokes equations when they are subjected to a leak boundary condition. He also derived a new convergence rate of the domain-decomposition method.M. Yamada and K. Ohkitani discovered, by a numerical experiments, a time-periodic solution, which simulate the turbulent motions of real flows. Less

（1）Navier-Stokes上的新现象是具有内部层的溶液和具有K-10光谱的THOSS溶液（2）表面波中的分叉现象。孤独的波（4）应用于反应 - 扩散系统，（5）由y. yz yz yz yz yz yz yz的涡流中的涡流。 10光谱在流体力学中趋向于无穷大。鲱鱼在旋转的液体中脱离了旋转的分流。在称为OSEEN的Navier-Stokes方程中，某些内部层被证明是H. Ikeda也证明了Tokes方程乳清的溶液中的HOPF双fur骨域分解方法的衍生速率

项目成果

H.Okamoto, M.Shoji: "World Scientific Publ."A Mathematical Introduction to Permanent Periodic Progressive Waves. 228 (2001)

H.Okamoto、M.Shoji：“世界科学出版社”永久周期行进波的数学简介。

H.Okamoto and X.Chen: "Global Existence of Solutions to the Proudman-Johnson Equation"Proc.Japan Acad.. 76. 149-152 (2000)

H.Okamoto 和 X.Chen：“Proudman-Johnson 方程解的全局存在性”Proc.Japan Acad.. 76. 149-152 (2000)

H.Ikeda and T.Ikeda: "Bifurcation phenomina from standing pulse solutions of bistable reaction-diffusion systems"J. Dynamics and Differential Equations (to appear). (2000)

H.Ikeda 和 T.Ikeda：“双稳态反应扩散系统的固定脉冲溶液的分叉现象”J。

M.Nagayama, H.Okamoto, J.Zhu: "On the blow-up of some similarity solutions of the Navier-Stokes equations"to appear in Quader.di Mat..

M.Nagayama、H.Okamoto、J.Zhu：“关于纳维-斯托克斯方程的一些相似解的放大”出现在 Quader.di Mat..

M.Nagayama, H.Okamoto: "On the interior layer appearing in the similarity solutions of the Navier-Stokes equations"to appear in Japan J.Indust.Appl.Math..

M.Nagayama、H.Okamoto：“论纳维-斯托克斯方程相似解中出现的内层”发表于日本 J.Indust.Appl.Math..