Mathematical Modelling of Spatial Spread in Anisotropic Landscapes

点击翻译按钮获取中文摘要

The primary goal of my research is to investigate mathematical models for spread in anisotropic landscapes and their applications. Anisotropy refers to directional information in the environment, for example white matter fiber tracks in the brain, seismic lines and roads in forest habitats, or wind and slope directions in landscapes. I will focus on two types of models, transport equations on networks and anisotropic diffusion equations. Anisotropic diffusion models are characterized by a diffusion tensor, which describes the mobility of particles in different directions. The project will focus on a detailed qualitative analysis of these models and applications. The application to glioma growth will help us to obtain more accurate tumor growth predictions, which can then be used for treatment planning. The application to forest fires is part of a new generation of forest fire prediction tools. And finally, an application to wolf movement in habitats with seismic lines will enable us to inform policy makers of strategies to reduce the impact of these seismic lines on the wolf hunting behavior.