In dieser Arbeit werden die Navier-Stokes Gleichungen für instationäre inkompressible Fluide in einem zeitabhängigen Gebiet untersucht. Das Verhalten des Fluids beeinflusst die Geometrie des Gebietes, indem das Fluid Kräfte (beschrieben durch den Spannungstensor) auf die deformierbare Struktur ausübt. Die Motivation dazu stammt aus de mathematischen Medizin - Simulation des Blutflusses in Arterien und Venen. Nach der Auswahl des passenden Modells für den Fluss innerhalb des Kanals mit viskoelastisch-deformierbaren Wänden, wird das Gesamtmodell mathematisch untersucht. Die Existenz schwacher Lösungen wird mithilfe der schwach-kompressiblen Approximation im Gebiet mit gegebener Deformationsfunktion nachgewiesen. Hierbei wir die Fluid-Struktur-Kopplungsbedingung mithilfe des Ansatzes für teilweise permeable Wände approximiert und somit entkoppelt. Schließlich werden numerische Experimente präsentiert, welche die Konvergenz der Iterationen bezüglich der Funktion der Deformation, wie auch das Verhalten der beweglichen Wand für sinkende Wandpermeabilität illustrieren.

This dissertation provides an interdisciplinary contribution to the project ReGLaN-Health & Logistics. ReGLaN-Health & Logistics, is an international cooperation deriving benefits from the capabilities of scientists working on different fields. The aim of the project is the development of a socalled SDSS that supports decision makers working within health systems with a special focus on rural areas. In this dissertation, one important component for the development of the DSS named EWARS is proposed and described in detail. This component called SPATTB is developed with the intention of dealing with spatial data, i.e. data with additional geocoded information with regard to the special requirements of the EWARS.rnrnAn important component in the process of developing the EWARS is the concept of GIS. Classically, geocoded information with a vectorial character numerically describing spatial phenomena is managed and processed in a GIS. For the development of the EWARS, the manageability of the type of data exemplarily given by (x,y,o) with coordinates x,y ) and Ozon-concentration o is not sufficient. It is described, that the manageable data has to be extended to data of type (x,y,f ), where (x,y) are the geocoded information, but where f is not only a numerical value but a functional description of a certain phenomenom. An example for the existence and appearance of that type of data is the geocoded information about the variation of the Ozon-concentration in time or depending on temperature. A knowledge-base as important subsystem of DSS containing expert knowledge is mentioned. This expert-knowledge can be made manageable when using methods from the field of fuzzy logic. Thereby mappings, socalled fuzzy-sets, are generated. Within the EWARS, these mappings will be used with respect to additional geocoded data. The knowledge about the geocoded mapping information only at a finite set of locations (x,y) associated with mapping information f is not sufficient in applications that need continuous statements in a certain geographical area. To provide a contribution towards solving this problem, methods from the field of computer geometry and CAD, so-called Bezier-methods, are used for interpolating this geocoded mapping information. Classically, these methods operates on vectors a the multidimensional vector-space whose elements contain real-valued components but in terms of dealing with mapping information, there has to be an extension on topological vector spaces since mapping spaces can be defined as such spaces. This builds a new perspective and possibility in the application of these methods. Therefore, the according algorithms have to be extended; this work is presented. The field of Artificial Neural Networks plays an important role for the processing and management of the data within the EWARS, where features of biological processes and structures are modeled and implemented as algorithms. Generally, the developed methods can be divided as usable in terms of interpolation or approximation functional coherences and in such being applicable to classification problems. In this dissertation one method from each type is regarded in more detailed. Thereby, the classical algorithms of the so-called Backpropagation-Networks for approximation and the Kohonen-Networks for classification are described. Within the thesis, an extension of these algorithms is then proposed using coherences from mathematical measure-theory and approximation theory. The mentioned extension of these algorithms is based on a preprocessing of the mapping data using integration methods from measure theory.