Nonlinear partial differential equations: Theoretical and numerical analysis

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Many physical phenomena are modelled by partial differential equations, and nonlinearities are essential for a realistic description. For evolving surfaces or interfaces, interesting behaviour like singularity formation is strongly linked to the nonlinear structure of the equations involved. The main topics of the research group are: -geometric evolution equations (Willmore flow and related fourth order parabolic flows, minimal hypersurfaces in Minkowski space,-minimal and holomorphic laminations (complex lines in tame almost comlex tori, minimal orbits and Hamilton-Jacobi equations,-nonlinear effects in fluids (generalized Newtonian and electrorheological fluids, fluids with cappilary free boundaries, physe transitions in thermoelasticity and compressible fluids).The common goal is to develop methods for solving the related equations, in a close interplay between theoretical and numerical analysis. The underlying mathematical difficulties often have a common source. The analysis of those problems will lead to an improved understanding of the nonlinear mechanisms, and the mathematical tools to be developed are relevant to future applications.http://home.mathematik.uni-freiburg.de/fg/Der Text der Zusammenfassung ist der oben angegebenen Seite zu entnehmen. Die Angabe des Links ist ausreichend.