Overview
Topic status: In progress
Overview
For some ill-posed models in applied mathematics we are fortunate that exact solutions are known for certain initial data. Typically, these solutions exist for a finite amount of time, after which they end abruptly at some sort of nasty blow-up. It is interesting to track the time-dependent behaviour of singularities of these exact solutions which appear in the complex plane. As these singularities do not appear to correspond to physical behaviour (they are, after all, in the complex plane), it may seem appropriate to disregard their importance to the physical problem. However, it turns out that these singularities play a very important role in determining the eventual behaviour of the physical problem, and in fact can shed light on the manner in which the solutions do or do not blow-up in finite time. The project is about exploring these issues.
Research activities
The project will involve complex variable theory with a touch of formal asymptotics.
Expected outcomes
The student will give a seminar at the end of the Summer.
Duration of project
6 weeks
- Study level
- Vacation research experience scholarship
- Supervisors
- QUT
- Organisational unit
Science and Engineering Faculty
- Research area
- Contact
- Please contact the supervisor for enquiries.
Associate Professor Scott McCue
