Teaching

Unit information

Synopsis

Partial Differential Equations are ubiquitous in the modelling of physical phenomena. This topic will introduce the modern theory of partial differential equations of different types, in particular the existence of solutions in an appropriate space. Fourier analysis, one of the most powerful tools of modern analysis, will also be covered. The following topics are covered in the unit:  Fourier transform, Distribution theory, Littlewood-Paley dyadic decompositions, Sobolev spaces theory, nonlinear Schrodinger equation (NLS), Strichartz estimates, Variational calculus and NLS; Periodic functions and Fourier series, Well-posedness of nonlinear Schrödinger equations (NLS) with either  periodic initial data, Brownian motion, well-posedness of stochastic NLS, Fourier restriction norm method, probabilistic Cauchy theory for the three-dimensional cubic non- linear wave equation, singular stochastic NLW

Mode of delivery

Clayton (On-campus)

Online (For external ACE students) if needed

Workload requirements

●  3 hours of seminars and 1 hour applied class per week

●  10 hours of independent study per week

Prerequisites 

MTH3160 (Functional analysis)

MTH4099 (Measure theory)

For the prerequisites, we recommend the following reference: Foundations of modern analysis, by Friedman, Avner

Unit Coordinator(s)

Professor Zihua Guo

Dr. Justin Forlano

Chief Examiner(s)

Professor Zihua Guo

Lecturers

Week 1-8: Professor Zihua Guo

Week 9-12: Dr. Justin Forlano

Weekly Schedule