In my research I studied differential equations, which are ubiquitous in science and engineering. The equation I investigated has an application in biofilm modelling. These are bacterial colonies encapsulated by a self-produced sticky slime layer, such as dental plaque and the brown deposits in water pipes. 

Bacteria in biofilms are better protected against external factors. Most bacteria therefore form biofilms, including those that infect the human body. As a result, antibiotics may work less effectively. For this reason, among others, the investigation of biofilms is important. 

In the model I studied, biofilms are not a flat layer, but form complex mushroom-shaped structures. 

In this thesis, the mathematical theory for differential equations is extended to include the biofilm growth model. It is proven that the model has a unique solution for a wide range of initial values ​​and domains and that it has a good degree of continuity. This is an important fact that justifies the use of computer simulations based on this model.