US-Germany Cooperative Research: Center Manifolds and Stability of Nonlinear Partial Differential Equations

该奖项支持Yuri Latushkin和密苏里-哥伦比亚大学的学生与德国哈雷-维滕贝格大学数学与信息系的Jan Pruess合作。本提案的主题是几个领域的相互作用：应用偏微分方程、无限维动力系统、演化理论方程和线性算子半群、算子谱理论和谐波分析。这项研究将有助于我们理解非线性偏微分方程的不变流形的存在性，以及由非线性稳态方程线性化产生的线性算子半群的谱理论。当前项目的一个共同目标是让密苏里-哥伦比亚大学和哈雷大学的一组博士后和研究生参与由双方高级研究员进行的数学（现代分析和应用偏微分方程）合作项目。资金将使密苏里大学的几名研究生能够参加国际互联网研讨会。该项目的研究结果将报告给布朗大学、伊利诺伊大学芝加哥分校、北卡罗来纳大学教堂山分校、明尼苏达大学、德克萨斯大学奥斯汀分校、孟菲斯大学、佐治亚理工学院、密歇根州立大学、图宾根大学、卡尔斯鲁厄大学、乌尔姆大学和许多其他科学中心的研究人员并与他们进行讨论，并将在中央数学期刊上发表。

0338743LatushkinThis award supports Yuri Latushkin and students from the University Missouri-Columbia in a collaboration with Jan Pruess of the Department of Mathematics and Informatics at the University of Halle-Wittenberg, Germany. The topic of the proposal is an interplay of several fields: applied partial differential equations, infinite dimensional dynamical systems, theory of evolution equations and semigroups of linear operators, operator spectral theory, and harmonic analysis. The funded research will add to our understanding of the existence of invariant manifolds for nonlinear partial differential equations and to the spectral theory of semigroups of linear operators generated by the linearization of the nonlinear equations about steady states. A concommitant goal of the current project is to involve a group of postdocs and graduate students at the University of Missouri-Columbia and the University of Halle in collaborative projects in mathematics (modern analysis and applied partial differential equations) conducted by the senior investigators on both sides. Funding will enable several graduate students at the University of Missouri to participate in the International Internet Seminar. The results of this project will be reported to and discussed with researchers at Brown University, University of Illinois at Chicago, University of North Carolina at Chapel Hill, University of Minnesota, University of Texas-Austin, University of Memphis, Georgia Institute of Technology, Michigan State, University of Tuebingen, University of Karlsruhe, University of Ulm, and many other scientific centers, and will be published in central mathematical journals.