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

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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.