Structured population dynamics is a central part of mathematical biology. In any realistic mathematical model of populations it is natural to assume that individuals differ with respect to some characteristic. This may be chronological age, size, or any other structuring variable such as level of infectiousness. In this project the student will learn about a state of the art issue, which is of current interest to the biological/life science community, and then build structured population models and analyze them to help shed light on important underlying biological phenomena.
Structured population models are often very challenging from the mathematical point of view. Even for a basic size-structured Gurtin-McCamy type of model, which takes the form of a quasilinear hyperbolic PDE with nonlinear and nonlocal boundary condition, the Principle of Linearised Stability has not been established to date. In this project the focus will be on gaining familiarity with some functional analytic techniques, such as the theory of semigroups of operators and the spectral theory of positive operators. Qualitative questions, such as asymptotic behavior of solutions, will be addressed as central fixture.