Mathematics

Advanced Partial Differential Equations (L.6)

Module code: G5215
Level 6
15 credits in spring semester
Teaching method: Lecture
Assessment modes: Unseen examination, Coursework

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 functional analysis, this module studies linear second-order elliptic, parabolic, and hyperbolic equations such as the potential, diffusion, and wave equations arising in inhomogeneous media.

You will then turn to the study of nonlinear PDE, focusing on calculus of variation.

Module learning outcomes

  • Understand the basic theory of Sobolev spaces and properties of Sobolev functions and be able to apply central theorems to partial differential equations (PDEs).
  • Understand the concept of weak solution and deploy established techniques for determining well-posedness of elliptic equations of the second order, evaluate regularity and apply maximum principle.
  • Understand, apply and discuss the theory of parabolic equations of the second order as well as linear, time-dependent equations.
  • Understand, apply and discuss the theory of calculus of variations, in particular explain the concept of a minimiser and discuss the regularity of minimisers.