An Infinite Dimensional Linear Fast-Reaction SystemMI 02.08.011 (Boltzmannstr. 3, 85748 Garching)

In this presentation I give an insight on the connections between finite and infinite Fast-Slow systems by showing that an infinite dimensional Fast-Slow system behaves like a finite dimensional one. To this extend I analyze a specific parameter dependent PDE, which can be considered as a linear Fast-Reaction system. More precisely, I show with the help of Fourier Transforms the convergence of the system to a limit system and proof an infinite dimensional version of the Tikhonov-Fenichel theorem using the possibility to explicitly construct infinite dimensional slow manifolds in the linear case.