Advanced Partial Diffrential Equations (G5215)
15 credits, Level 6
You will be introduced to modern theory of linear and nonlinear Partial Differential Equations. Starting from the theory of Sobolev spaces and relevant concepts in linear operator theory, which provides the functional analytic framework, you will treat the linear second-order elliptic, parabolic, and hyperbolic equations (Lax-Milgram theorem, existence of weak solutions, regularity, maximum principles), e.g., the potential, diffusion, and wave equations that arise in inhomogeneous media. The emphasis will be on the solvability of equations with different initial/boundary conditions, as well as the general qualitative properties of their solutions. You will then turn to the study of nonlinear PDE, focusing on calculus of variation.
20%: Coursework (Problem Set)
80%: Examination (Unseen examination)
Contact hours and workload
This module is 150 hours of work. This breaks down into 33 hours of contact time and 117 hours of independent study.
This module is running in the academic year 2019/20. We also plan to offer it in future academic years. It may become unavailable due to staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of such changes to modules at the earliest opportunity.