Partial Differential Equations in Cancer Modelling

Cancer is not just one disease, but rather a complicated interaction of many abnormal features and many different cell types, which are situated in a heterogeneous habitat of normal tissue. The mathematical modelling of cancer growth and treatment is at full swing, and a significant challenge arises due to the interactions of cancer with a complicated and structured microenvironment of healthy tissue. Many of the spatial models in cancer modelling are based on partial differential equations (PDEs) that include spatial heterogeneity, orientational tissue structure, tissue stiffness and deformability. The analysis of these coupled non-linear PDEs is challenging. Specific problems relate to reaction-diffusion equations, transport equations, continuum equations, and to their local and global existence and uniqueness, pattern formation, invasion, free boundary problems, anisotropic diffusion, and control. In this workshop we gathered leading experts and young researchers from PDE modelling in mathematics, medicine and biology to discuss the analysis and application of PDE models for cancer and cancer treatment.