Module Information
Course Delivery
| Delivery Type | Delivery length / details |
|---|---|
| Lecture | 16 Hours. (16 x 1 hour lectures) |
| Seminars / Tutorials | 4 Hours. (4 x 1 hour example classes) |
Assessment
| Assessment Type | Assessment length / details | Proportion |
|---|---|---|
| Semester Assessment | coursework | 100% |
| Supplementary Assessment | coursework | 100% |
Learning Outcomes
On completion of this module, students should be able to:
1. explain the concept of a weak derivative.
2. calculate the weak formulation of a partial differential equation.
3. state and apply the Lax-Milgram Theorem.
4. classify the set of partial differential equations arising from a range of differential constitutive equations.
5. explain what is meant by a bifurcation.
6. explore and describe the stability of a number of viscoelastic flows.
7. explain possible causes of material instability and melt fracture.
8. examine and describe the formation of elastic boundary layers.
9. analyse the nature of the singular behaviour of solutions in regions of the flow near reentrant corners.
Brief description
This module develops techniques for the analysis of mathematical problems in nonlinear viscoelasticity by first introducing concepts from the modern theory of partial differential equations, and then specialising to problems for complex fluids. The systems of governing partial differential equations will be analysed to provide information on existence and uniqueness of solutions, the classification of the system and possible change of type. In addition, topics selected from the formation of elastic boundary layers, the flow near a reentrant corner, the stability of viscoelastic flows, material instability and melt fracture, will be examined in some detail.
Aims
This module will introduce techniques from the modern theory of partial differential equations and apply them to a number of mathematical problems in nonlinear viscoelasticity including existence and uniqueness of solutions to the governing sets of partial differential equations, change of type, flow stabilities, corner singularities and stress boundary layers.
Reading List
Recommended TextD.D.Joseph (1990) Fluid dynamics of viscoelastic liquids Springer-Verlag Primo search M Renardy (2000) Mathematical analysis of viscoelastic flows SIAM Primo search R. G. Owens and T. N. Phillips (2002) Computational Rheology Imperial College Press Primo search Supplementary Text
Evans, Lawrence C. (2004) Partial Differential Equations Primo search
Notes
This module is at CQFW Level 7