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Formation of Singulatiries in Solutions of Nonlinear Schrodinger Equations and Related Fields

非线性薛定谔方程解中奇异点的形成及相关领域

基本信息

批准号：
14340054
负责人：
NAWA Hayato
金额：
$ 7.3万
依托单位：
Osaka University (2004-2005)Nagoya University (2002-2003)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2005
项目状态：
已结题

项目摘要

Nawa and Ishige (collaboration with Ishiwata and Sakajo) organizes a seminar (http://www.gifu-u.ac.jp/~tisiwata/seminar/ma_seminar.html) ; we had many opportunities to have discussions and interactions with researchers from several fields of mathematical sciences through the seminar.For blowup solutions of the pseudo-conformally invariant nonlinear Schrodinger equation (pc-NLS), Nawa obtain some relation between their asymptotic behavior and blowup rates. This result enable him to launch into a full-dress investigation of blowup rate via the Nelson process behind the solution. He also obtain some analogous results on the derivative nonlinear Schrodinger equation. It turns out that the method developed for pc-NLS is useful for investigating a coupled system of NLS which is modeled on the BCS reduced Hamiltonian in a classical context ; we can see pair-creation in solutions of this classical field equation.Ishige succeeded to characterize the blowup set for semilinear heat equations with … More Neuman boundary conditions. He also investigated the hot spot movement of solutions of the linear heat equation on the exterior domain of a ball under the Dirichlet or Neuman boundary conditions. In the course of the study, he obtain useful results to make further investigation into the asymptotic behavior of solutions for more general reaction diffusion equations.Among other his results on several fields of mathematical sciences, Suzuki made an interesting study on self-dual gauge field equations via blowup analysis, and on blowup problem for simplified system of chemotaxis ; continuation of the solution after blowup, blowup in infinite time, etc.Ogawa developed a theory on the topological verification for numerical analysis via Conley index to obtain rigorous results for formation of localized patterns in solutions to the quintic Swift-Hohenberg equation. He also investigated the oscillatory behavior in an Electrochemical reaction diffusion system ; he conducted a bifurcation analysis with an aid of numerical analysis. Less

纳瓦和Ishige（与Ishiwata和Sakajo合作）组织了一个研讨会（http：//www.gifu-u.ac.jp/Aktisiwata/Aktisar/ma_Aktisar.html），我们有很多机会通过研讨会与来自数学科学各个领域的研究人员进行讨论和互动。对于伪共形不变非线性薛定谔方程（pc-NLS）的爆破解，纳瓦得到了它们的渐近行为与爆破速率之间的一些关系。这个结果使他能够通过解背后的纳尔逊过程对爆破率进行全面的研究。对导数非线性薛定谔方程也得到了类似的结果。结果表明，对于以BCS约化哈密顿量为模型的耦合NLS系统，我们可以用pc-NLS方法来研究;在这个经典场方程的解中，我们可以看到对的产生。Ishige成功地刻画了半线性热方程的爆破集， ...更多信息 Neuman边界条件他还研究了热点运动的解决方案的线性热方程的外部域的一个球的狄利克雷或纽曼边界条件。在研究过程中，他得到了一些有用的结果，对更一般的反应扩散方程解的渐近性态作了进一步的研究，其中Suzuki对自对偶规范场方程的爆破分析和简化趋化系统的爆破问题作了有趣的研究;解在爆破后的延续、无限时间内的爆破等。Ogawa发展了一种关于通过Conley指数进行数值分析的拓扑验证的理论，以获得在五次Swift-Hohenberg方程的解中形成局部模式的严格结果。他还研究了振荡行为的电化学反应扩散系统，他进行了分叉分析的援助，数值分析。少