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

0338743 Latushkin这个奖项支持尤里Latushkin和学生从密苏里大学哥伦比亚在一个合作与扬普鲁斯的数学和信息学系在哈雷-维滕贝格大学，德国。 该提案的主题是几个领域的相互作用：应用偏微分方程，无穷维动力系统，理论的发展方程和半群的线性算子，算子谱理论，调和分析。 资助的研究将增加我们对非线性偏微分方程的不变流形的存在性的理解，并增加对线性算子半群的谱理论的理解，所述线性算子半群由关于稳态的非线性方程的线性化产生。 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双方高级研究人员进行的数学合作项目（现代分析和应用偏微分方程）。 资金将使密苏里州大学的几名研究生能够参加国际因特网研讨会。 该项目的结果将报告给布朗大学、伊利诺伊大学芝加哥分校、查佩尔山的北卡罗来纳州大学、明尼苏达大学、得克萨斯大学奥斯汀分校、孟菲斯大学、格鲁吉亚理工学院、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.