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Research Activity

I mainly work with partial differential equations (PDE) used for

describing various dynamic phenomena, i.e. processes that involve changes in space and time.

Central issues in this research activity are:

Development of appropriate mathematical models in terms of systems of partial differential equations (PDE) motivated by concrete applications;

Development of suitable discrete versions of the PDEs in question (numerical methods) and mathematical analysis of their properties in order to ensure convergence to the correct solutions;

Comparison with experimental data in order to evaluate the proposed models and gain information for further development, i.e. seek to build finer mechanisms into the models;

Application of mathematical analysis that can provide insight into qualitative properties possessed by the solutions of these models. Fundamental issues like existence, uniqueness, and stability of solutions are included, as well as the study of analytical solutions and asymptotic behaviour (long-time behaviour).

A main goal is the development of simplified models that can be used for extracting deeper

insight into complicated problems that cannot easily be studied by relying only on available

commercial simulators. Comparison and evaluation of models against experimental data

(lab experiments) represent a crucial aspect of such mechanistic studies. More concrete

examples from different fields are given below.

Some of the applications we focus on are highly relevant for the petroleum

industry, however, the models we work with are by no means restricted to that only. In

other words, there is ample of room for synergy effects between these petroleum related

applications and totally different applications within other fields like chemical engineering, earth science, theoretical biology, and material science, to mention a few.

Different Models

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