Studies on singular perturbation problems in nonlinear mechanics

(1)发现了Navier-Stokes方程的新现象。其中，具有内层的溶液和具有k-10光谱的溶液是值得注意的。(2)阐明了表面波中的分叉现象。特别地，发展了奇异孤立波的精确数值方法。(3)强化了Ohkitani和Yamada提出的湍流壳模型的动力系统观点。(4)在反应扩散系统中的应用；(5)木村在二维衰变湍流中的旋涡形成。(6)Kawashima和MatSumura阐明了激波解的渐近行为，Okamoto在Kim Sunchul的帮助下分析了菱形周期流中的分支解。数值计算表明，当雷诺数趋于无穷大时，某些解具有k-10谱。Okamoto和A.Craik认为，流体力学中出现了一个三维动力系统。两个不同的…找到了更多的解，一个有90度弯曲的解，一个没有弯曲的解，并从理论上解释了它们的机理。Y.Kimura和J.Herring成功地解释了旋转流体中产生的涡旋结构的理论背景。S.Kawashima证明了辐射气体的适定性，T.Ikeda考虑了燃烧合成模型。通过数值实验，他证明了模型的解可以重现实验室实验的结果。池田和冈本考虑了N-S方程的一种特殊解，称为欧森流。一些内部层面得到了严格的证明。H.Ikeda还证明了一类双稳态反应扩散系统的行波解存在Hopf分支。H.Fujita证明了当Navier-Stokes方程满足泄漏边界条件时，解的存在性。M.Yamada和K.Ohkitani通过数值实验发现了一个时间周期解，它模拟了真实流动的湍流运动。较少

(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