Welcome

to the webpages of the Applied Analysis group

A main concern of Applied Analysis is the mathematical treatment of models arising in natural sciences such as Physics, Biology, Medicine, Pharmaceutics, Chemistry, engineering sciences, economic sciences, sociology, etc.

The research area of Applied Analysis resides hence somewhere in between pure mathematics and concrete applications. Many processes occuring in natural sciences such as diffusion (e.g. heat propagation) or fluid flow can (somewhat simplified) be described by evolution equations of the form

                u'-Au=f

with a certain 'so-called' operator A.
The applied analyst examines properties of such an equation concerning existence, uniqueness, and regularity of solutions. In addition stability issues are of preferential interest, in order to
determine the long-term behavior of a solution. This provides important information, e.g., on the trend of stock prices or the influence of medication on the course of a disease.

For the applied scientist this yields important feedback on well-posedness and asymptotics of the underlying model, which helps him in adapting, further developing, and improving the model. By this fact, the modeling itself is usually also within the research scope of the applied Analyst.

In the examination of various phenomena the corresponding models often display common structural properties. Taking advantage of this fact the applied analyst developes methods and tools that apply to a wide class of problems. This requires deep tools from a number of mathematical branches such as, e.g., functional analysis, harmonic analysis, Banach space geometry, varational calculus, operator theory, theory on partial differential equations, etc. Especially the further development of these branches and resulting tools represents an essential element in our research. In this way, Applied Analysis also links theoretical mathematics to more applied sciences.